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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{sec ^{2} ( x )}{tan ^{2} ( x )}

Express with sin, cos

= \frac{1}{sin ^{2} ( x )}

Manipulating right side

1 + cot^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ^{2} ( x )}

We showed that the two sides could take the same form

\Rightarrow True

cos (2 θ) = \frac{csc ^{2} ( θ ) - 2}{csc ^{2} ( θ )}

tan (a) = \frac{1}{cot ( a )}

cos^{4} (x) + sin^{4} (x) = 1

tan^{2} (x) csc^{2} (x) = 1 + tan^{2} (x)

sin (x) = - sin (- x)

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