Using Sum and Product Identities

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1

Simplify $\sin x\cot x$ .

CORRECT

$\csc x$

0

$\tan x$

0

$\sin x \cos x$

0

$\cos^2x$

0

Explanation

To simplify $\sin x\cot x$ , break them into their SOHCAHTOA parts:

$\frac{\text{opposite}}{\text{hypotenuse}}*\frac{\text{adjacent}}{\text{opposite}}$ .

Notice that the opposite's cancel out, leaving $\frac{\text{adjacent}}{\text{hypotenuse}}=\cos x$ .

2

Simplify $\csc x \tan x$ .

$\sec x$

CORRECT

$\cos x$

0

$\sin x \cos x$

0

0

This is the most simplified version.

0

Explanation

Break down $\csc x \tan x$ into SOHCAHTOA to solve:

$\csc=\frac{\text{hypotenuse}}{\text{opposite}}$ and $\tan=\frac{\text{opposite}}{\text{adjacent}}$ .

Therefore, $\csc x \tan x=\frac{\text{hypotenuse}}{\text{opposite}}*\frac{\text{opposite}}{\text{adjacent}}$ . Note that the opposite's cancel out, leaving $\frac{\text{hypotenuse}}{\text{adjacent}}$ , which is the same as $\sec x$ .

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