Is (sin(θ))/(csc(θ)-cot(θ))=1+cos(θ) ?

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

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prove (sin(θ))/(csc(θ)-cot(θ))=1+cos(θ)

prove

\frac{sin ( θ )}{csc ( θ ) - cot ( θ )} = 1 + cos (θ)

True

Solution steps

\frac{sin ( θ )}{csc ( θ ) - cot ( θ )} = 1 + cos (θ)

Manipulating left side

\frac{sin ( θ )}{csc ( θ ) - cot ( θ )}

Express with sin, cos

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

Rewrite using trig identities

= cos (θ) + 1

= 1 + cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

cot (- a) cos (- a) + sin (- a) = - csc (a)

sin (2 a) - tan (a) = tan (a) cos (2 a)

2 cos (x) tan (x) csc (x) = 2

sec^{2} (y) - cot^{2} (\frac{π}{2} - y) = 1

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