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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

Rewrite using trig identities

tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{2 tan ( θ )}{1 + tan ^{2} ( θ )} = sin (2 θ)

tan^{2} (θ) sin^{2} (θ) = tan^{2} (θ) - sin^{2} (θ)

cos (x) (sec (x) - cos (x)) = sin^{2} (x)

cos (z + w) = cos (z) cos (w) - sin (z) sin (w)

(1 - cos^{2} (θ)) csc^{2} (θ) = 1

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