Is 1/(1+cos(x))=csc^2(x)-csc(x)cot(x) ?

The answer to whether 1/(1+cos(x))=csc^2(x)-csc(x)cot(x) is True

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prove 1/(1+cos(x))=csc^2(x)-csc(x)cot(x)

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( x ) + 1}

= \frac{1}{1 + cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

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

sin (\frac{A}{2}) = \frac{1}{2} sin (A)

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

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

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

Is 1/(1+cos(x))=csc^2(x)-csc(x)cot(x) ?
The answer to whether 1/(1+cos(x))=csc^2(x)-csc(x)cot(x) is True