High School Math : Using Identities of Squared Functions

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #9 : Trigonometric Identities

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

Possible Answers:

\(\displaystyle \cos^2 x+3\)

\(\displaystyle \csc x\)

\(\displaystyle \sin x+3\)

This is already it's most reduced form.

\(\displaystyle \sin x \cos x\)

Correct answer:

\(\displaystyle \sin x+3\)

Explanation:

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

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

This leaves us with \(\displaystyle \sin x +3\).

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