Is (tan^2(θ))/(sin(θ))=sec(θ)tan(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ^{2} ( θ )}{sin ( θ )}

Express with sin, cos

= \frac{sin ( θ )}{cos ^{2} ( θ )}

Manipulating right side

sec (θ) tan (θ)

Express with sin, cos

= \frac{sin ( θ )}{cos ^{2} ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

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

sin (2 x) + sin (2 y) = 2 sin (x + y) cos (x - y)

sin (θ) csc (θ) cos (θ) = cos (θ)

cot (x) - csc^{2} (x) cot (x) = - cot^{3} (x)

cot (x - \frac{π}{2}) = - tan (x)

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