Is (cos(θ))/(1-sin(θ))=tan(θ)+sec(θ) ?

The answer to whether (cos(θ))/(1-sin(θ))=tan(θ)+sec(θ) is True

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prove (cos(θ))/(1-sin(θ))=tan(θ)+sec(θ)

prove

\frac{cos ( θ )}{1 - sin ( θ )} = tan (θ) + sec (θ)

True

Solution steps

\frac{cos ( θ )}{1 - sin ( θ )} = tan (θ) + sec (θ)

Manipulating right side

tan (θ) + sec (θ)

Express with sin, cos

= \frac{1 + sin ( θ )}{cos ( θ )}

Rewrite using trig identities

= \frac{cos ( θ )}{1 - sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

\frac{2 cos ( 2 θ )}{sin ( 2 θ )} = cot (θ) - tan (θ)

sin^{2} (x) cos^{2} (x) + cos^{4} (x) = cos^{2} (x)

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

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

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

Is (cos(θ))/(1-sin(θ))=tan(θ)+sec(θ) ?
The answer to whether (cos(θ))/(1-sin(θ))=tan(θ)+sec(θ) is True