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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Manipulating right side

cot (t) + tan (t)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

csc (\frac{π}{2} - x) = sec (x)

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

2 sin^{2} (x) + cos (2 x) = 1

\frac{1 + sec ( x )}{sin ( x ) + tan ( x )} = csc (x)

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

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