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High School Math : Using Identities of Squared Functions

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Example Question #1 : Using Identities Of Squared Functions

Factor and simplify $\frac{\sin^2x-9}{\sin x-3}$ $\displaystyle \frac{\sin^2x-9}{\sin x-3}$ .

Possible Answers:

$\cos^2 x+3$ $\displaystyle \cos^2 x+3$

$\sin x \cos x$ $\displaystyle \sin x \cos x$

$\csc x$ $\displaystyle \csc x$

This is already it's most reduced form.

$\sin x+3$ $\displaystyle \sin x+3$

Correct answer:

$\sin x+3$ $\displaystyle \sin x+3$

Explanation:

To reduce $\frac{\sin^2x-9}{\sin x-3}$ $\displaystyle \frac{\sin^2x-9}{\sin x-3}$ , factor the numerator: $\frac{(\sin x-3)(\sin x+3)}{\sin x-3}$ $\displaystyle \frac{(\sin x-3)(\sin x+3)}{\sin x-3}$

Notice that we can cancel out a $\sin x -3$ $\displaystyle \sin x -3$ .

This leaves us with $\sin x +3$ $\displaystyle \sin x +3$ .

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High School Math : Using Identities of Squared Functions

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Example Question #1 : Using Identities Of Squared Functions

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