Is (sec^2(θ))/(tan(θ))=sec(θ)csc(θ) ?

The answer to whether (sec^2(θ))/(tan(θ))=sec(θ)csc(θ) is True

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prove (sec^2(θ))/(tan(θ))=sec(θ)csc(θ)

prove

\frac{sec ^{2} ( θ )}{tan ( θ )} = sec (θ) csc (θ)

True

Solution steps

\frac{sec ^{2} ( θ )}{tan ( θ )} = sec (θ) csc (θ)

Manipulating left side

\frac{sec ^{2} ( θ )}{tan ( θ )}

Express with sin, cos

= \frac{1}{cos ( θ ) sin ( θ )}

Rewrite using trig identities

sec (θ) csc (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

cos^{2} (x) - sin^{2} (x) = cos (2 x)

sec^{2} (θ) (1 - cos^{2} (θ)) = tan^{2} (θ)

cos^{2} (θ) + tan^{2} (θ) cos^{2} (θ) = 1

Is (sec^2(θ))/(tan(θ))=sec(θ)csc(θ) ?
The answer to whether (sec^2(θ))/(tan(θ))=sec(θ)csc(θ) is True