Is (1+cos(t))/(1-cos(t))=(csc(t)+cot(t))^2 ?

The answer to whether (1+cos(t))/(1-cos(t))=(csc(t)+cot(t))^2 is True

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prove (1+cos(t))/(1-cos(t))=(csc(t)+cot(t))^2

prove

\frac{1 + cos ( t )}{1 - cos ( t )} = (csc (t) + cot (t))^{2}

True

Solution steps

\frac{1 + cos ( t )}{1 - cos ( t )} = (csc (t) + cot (t))^{2}

Manipulating right side

(csc (t) + cot (t))^{2}

Express with sin, cos

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

Rewrite using trig identities

= \frac{1 + cos ( t )}{1 - cos ( t )}

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (α) + csc^{2} (α) = \frac{1}{sin ^{2} ( α ) cos ^{2} ( α )}

sin^{2} (A) + cos^{2} (A) = 1

tan (x) = sin (x) sec (x)

(1 + cot^{2} (θ)) (1 - cos^{2} (θ)) = 1

csc (2 x) + cot (2 x) = cot (x)

Is (1+cos(t))/(1-cos(t))=(csc(t)+cot(t))^2 ?
The answer to whether (1+cos(t))/(1-cos(t))=(csc(t)+cot(t))^2 is True