Sum and Difference Identities For Cosine - Pre-Calculus

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Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

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$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

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Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

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$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

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Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

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Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

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$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

Tap to see back →

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

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$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Tap to see back →

Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Tap to see back →

Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

Use the sum or difference identity to find the exact value: $cos255^\circ$

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Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

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$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Tap to see back →

Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Tap to see back →

Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

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$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

Tap to see back →

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

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$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Tap to see back →

Using the identity, we can break up the into and then solve: $\cos 300\cdot \cos 45+\sin 300\cdot \sin 45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ and so the correct answer is $$\frac{\sqrt{2}$-$\sqrt{6}$}{4}$ .

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Tap to see back →

Here we break up the into and solve using the sin identity: $\sin 135\cdot \cos 30+\cos 135\cdot \sin 30\rightarrow $\frac{\sqrt{2}$}2{}\cdot $\frac{\sqrt{3}$}2{}+\frac{-\sqrt{2}$}2{}\cdot $\frac{1}{2}\rightarrow $\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ and so here the credited answer is $$\frac{\sqrt{6}$-$\sqrt{2}$}{4}$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

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$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Sum and Difference Identities For Cosine - Pre-Calculus

Is the following equation an identity?

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Is the following equation an identity?

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Is the following equation an identity?

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the 255 into and then solve:

Is the following equation an identity?

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value:

Using the identity, we can break up the into and then solve: and so the correct answer is .

Use the sum or difference identity to find the exact value of .

Here we break up the into and solve using the sin identity: and so here the credited answer is .

Is the following equation an identity?

Due to this inequality, this is not an identity.

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.

Use the sum or difference identity to find the exact value: $cos255^\circ$

Using the identity, we can break up the 255 into and then solve: $cos300\cdot cos45+sin300\cdot sin45\rightarrow $\frac{1}{2}$\cdot $\frac{\sqrt{2}$}{2}+\frac{-\sqrt{3}$}{2}\cdot $\frac{\sqrt{2}$}{2}\rightarrow $\frac{\sqrt{2}$-$\sqrt{6}$}{4}$

Is the following equation an identity? $cos(x-\pi)=cos(x)$

$cos(x-\pi)=cos(x)\rightarrow cosxcos\pi+sinxsin\pi=cosx\rightarrow cosx(-1)+sinx(0)=cosx\rightarrow -cosx\neq cosx$

and due to this inequality, this is not an identity

Use the sum or difference identity to find the exact value: $\cos $255^{\circ}$$

Use the sum or difference identity to find the exact value of $\sin $165^{\circ}$$ .

Is the following equation an identity?

$\cos \left ( x-\pi \right )=\cos \left ( x \right )$

$\cos \left ( x-\pi \right )=\cos \left ( x \right )\rightarrow \cos x\cos \pi +\sin x\sin \pi =\cos x\rightarrow \cos x(-1)+\sin x(0)=\cos x\rightarrow -\cos x\neq \cos x$

Due to this inequality, this is not an identity.