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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{sin ( θ )}{1 - cos ( θ )}

Rewrite using trig identities

= \frac{1 + cos ( θ )}{sin ( θ )}

Manipulating right side

csc (θ) + cot (θ)

Express with sin, cos

= \frac{1 + cos ( θ )}{sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (5 x) - sin^{2} (5 x) = cos (10 x)

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

tan (2 a) - tan (a) = tan (a) sec (2 a)

sin^{2} (x) - 4 cos^{2} (x) = 5 sin^{2} (x) - 4

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

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