Is (sin(θ))/(sin(θ)-1)= 1/(1-csc(θ)) ?

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

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prove (sin(θ))/(sin(θ)-1)= 1/(1-csc(θ))

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{1 - csc ( θ )}

Express with sin, cos

= \frac{sin ( θ )}{- 1 + sin ( θ )}

= \frac{sin ( θ )}{sin ( θ ) - 1}

We showed that the two sides could take the same form

\Rightarrow True

cot (x) (sec (x) - cos (x)) = sin (x)

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

cos (x + y) cos (x - y) = cos^{2} (x) - sin^{2} (x)

cos (2 θ) csc^{2} (θ) = csc^{2} (θ) - 2

cos (x) - cos (x) = 0

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