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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Manipulating right side

1 - cos (θ)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (x) cos^{2} (x) = cot^{2} (x)

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

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

cos^{2} (B) = \frac{1}{2} (1 + cos (2 B))

sin (θ + π) = - sin (θ)

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