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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ( θ )}

Rewrite using trig identities

csc (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (x) \cdot csc (x) = cot (x)

sin (4 x) = 4 sin (x) cos (x) cos (2 x)

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

sec (α) - cos (α) = sin (α) tan (α)

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