Using Pythagorean Identities - High School Math

Card 0 of 4

Question

Simplify

$\cot(x)\times{\sin(x) }$

Answer

$\cot(x) = \cos(x)/\sin(x)$ . Thus: $[\cos(x)/\sin(x)]\times\sin(x)=\cos(x)$

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Question

Simplify

$\frac{cot (x)\cdot tan(x)}{cos(x)}$

Answer

$\cot(x)\times\tan(x) = 1$

and

$1/(\cos(x)) = \sec(x)$ .

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Question

Simplify $\frac{\cos^2x-1}{\sin x}$ .

Answer

Remember that $\sin^2x+\cos^2 x=1$ . We can rearrange this to simplify our given equation:

$\frac{\cos^2x-1}{\sin x}$

$=\frac{-\sin^2x}{\sin x}=-\sin x$

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Question

Simplify:

$\sin^2x+\cos^2x+\tan^2x$

Answer

Whenever you see a trigonometric function squared, start looking for a Pythagorean identity.

The two identities used in this problem are $\sin^2 x + \cos ^2 x=1$ and $\tan^2 x +1 =\sec^2 x$ .

Substitute and solve.

$\sin^2x+\cos^2x+\tan^2x=?$

$(\sin^2x+\cos^2x)+\tan^2x=?$

$(1)+\tan^2x=\sec^2 x$

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