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 )}

Manipulating right side

\frac{sin ( θ )}{1 - cos ( θ )}

Rewrite using trig identities

= \frac{1 + cos ( θ )}{sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

1 + tan^{2} (- x) = sec^{2} (x)

tan (\frac{π}{2} - x) = cot (x)

sec (θ) = \frac{tan ( θ )}{sin ( θ )}

sec (x) cos (x) = 1

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

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