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

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

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

prove

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

True

Solution steps

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

Manipulating left side

csc (θ) - cot (θ)

Express with sin, cos

= \frac{1 - cos ( θ )}{sin ( θ )}

Rewrite using trig identities

= \frac{sin ( θ )}{1 + cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{sin ^{2} ( x )}{tan ^{2} ( x )} = cos^{2} (x)

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

tan (2 π - θ) = - tan (θ)

sin^{4} (θ) - cos^{4} (θ) = 1 - 2 cos^{2} (θ)

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