Is (sin^2(y))/(cos(y))=sec(y)-cos(y) ?

The answer to whether (sin^2(y))/(cos(y))=sec(y)-cos(y) is True

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prove (sin^2(y))/(cos(y))=sec(y)-cos(y)

prove

\frac{sin ^{2} ( y )}{cos ( y )} = sec (y) - cos (y)

True

Solution steps

\frac{sin ^{2} ( y )}{cos ( y )} = sec (y) - cos (y)

Manipulating right side

sec (y) - cos (y)

Express with sin, cos

= \frac{1 - cos ^{2} ( y )}{cos ( y )}

Rewrite using trig identities

= \frac{sin ^{2} ( y )}{cos ( y )}

We showed that the two sides could take the same form

\Rightarrow True

cot (θ) sec (θ) = csc (θ)

csc^{2} (θ) (1 - cos^{2} (θ)) = 1

cos^{2} (θ) + sin^{2} (θ) = 1

sin (\frac{3 π}{2} + θ) = - cos (θ)

(1 - cos^{2} (x)) (1 + tan^{2} (x)) = tan^{2} (x)

Is (sin^2(y))/(cos(y))=sec(y)-cos(y) ?
The answer to whether (sin^2(y))/(cos(y))=sec(y)-cos(y) is True