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

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

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prove (1+tan^2(θ))/(1+cot^2(θ))=tan^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

tan^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{cos ( θ )} - cos (θ) = tan (θ) sin (θ)

sin (x) = cos (x) tan (x)

sin (x) = cos (\frac{π}{2} - x)

sin (\frac{π}{2} - x) tan (x) = sin (x)

sin (X) sec (X) = tan (X)

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