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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \frac{1}{cos ( x ) sin ( x )}

Manipulating right side

tan (x) + cot (x)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( x ) sin ( x )}

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (A) (csc^{2} (A) - 1) = 1

cos^{3} (θ) = - 1

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

(tan (x)) (sin (x)) + (cos (x)) = sec (x)

cos (k (x) x) = cos (- k (x) x)

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