# How do you verify:cot^2x-cos^2x=cot^2xcos^2x?

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13
Mar 22, 2017

#### Explanation:

${\cot}^{2} x - {\cos}^{2} x$

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

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

= $\frac{{\cos}^{2} x \left(1 - {\sin}^{2} x\right)}{\sin} ^ 2 x$

= $\frac{{\cos}^{2} x \times {\cos}^{2} x}{\sin} ^ 2 x$

= $\left({\cos}^{2} \frac{x}{\sin} ^ 2 x \times {\cos}^{2} x\right)$

= ${\cot}^{2} x {\cos}^{2} x$

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

2
Nghi N. Share
Mar 22, 2017

Develop the left side:
$L S = \frac{{\cos}^{2} x}{{\sin}^{2} x} - {\cos}^{2} x = \frac{\left({\cos}^{2} x\right) \left(1 - {\sin}^{2} x\right)}{{\sin}^{2} x} =$
$= \frac{{\cos}^{2} x . {\cos}^{2} x}{{\sin}^{2} x} = {\cot}^{2} x . {\cos}^{2} x$ Proved.

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