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# How do you verify the identity 1/(1-tan^2theta)+1/(1-cot^2theta)=1?

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#### Explanation

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#### Explanation:

I want someone to double check my answer

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Bdub Share
Mar 9, 2018

See Below

#### Explanation:

$L H S : \frac{1}{1 - {\tan}^{2} \theta} + \frac{1}{1 - {\cot}^{2} \theta}$

$= \frac{1}{1 - {\tan}^{2} \theta} + \frac{1}{1 - \frac{1}{\tan} ^ 2 \theta}$

$= \frac{1}{1 - {\tan}^{2} \theta} + \frac{1}{\frac{{\tan}^{2} \theta - 1}{\tan} ^ 2 \theta}$

$= \frac{1}{1 - {\tan}^{2} \theta} + {\tan}^{2} \frac{\theta}{{\tan}^{2} \theta - 1}$

$= \frac{1}{1 - {\tan}^{2} \theta} - {\tan}^{2} \frac{\theta}{1 - {\tan}^{2} \theta}$->factor out -1

$= \frac{1 - {\tan}^{2} \theta}{1 - {\tan}^{2} \theta}$->common denominator

=cancel((1 - tan^2 theta)/(1-tan^2 theta)

$= 1$

$= R H S$

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