Is 1/(1-tan^2(x))+1/(1-cot^2(x))=1 ?

The answer to whether 1/(1-tan^2(x))+1/(1-cot^2(x))=1 is True

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prove 1/(1-tan^2(x))+1/(1-cot^2(x))=1

prove

\frac{1}{1 - tan ^{2} ( x )} + \frac{1}{1 - cot ^{2} ( x )} = 1

True

Solution steps

\frac{1}{1 - tan ^{2} ( x )} + \frac{1}{1 - cot ^{2} ( x )} = 1

Manipulating left side

\frac{1}{1 - tan ^{2} ( x )} + \frac{1}{1 - cot ^{2} ( x )}

Express with sin, cos

= 1

We showed that the two sides could take the same form

\Rightarrow True

tan (2 a) = \frac{2 tan ( a )}{1 - tan ^{2} ( a )}

csc (x) - cot (x) = \frac{1}{csc ( x ) + cot ( x )}

cos (π - θ) + sin (\frac{π}{2} + θ) = 0

sin (x) - csc (x) = - cos (x) cot (x)

tan (y) + cot (y) = sec (y) csc (y)

Is 1/(1-tan^2(x))+1/(1-cot^2(x))=1 ?
The answer to whether 1/(1-tan^2(x))+1/(1-cot^2(x))=1 is True