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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

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{1}{tan ( β )} + tan (β) = sec (β) csc (β)

\frac{cos ( 2 x )}{sin ( x )} = cos (x) cot (x) - sin (x)

cot^{2} (2 x) + cos^{2} (2 x) + sin^{2} (2 x) = csc^{2} (2 x)

sin^{2} (x) - 4 cos^{2} (x) = 1 - 5 cos^{2} (x)

25 sec^{2} (5 x) = 25 + (5 tan (5 x))^{2}

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