Is (1+cos(x))/(sin(x))=cot(x/2) ?

The answer to whether (1+cos(x))/(sin(x))=cot(x/2) is True

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prove (1+cos(x))/(sin(x))=cot(x/2)

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

\frac{1 + cos ( 2 u )}{sin ( 2 u )} = cot (u) :

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (a - b) - cos (a + b) = 2 sin (a) sin (b)

tan (θ) sin (θ) = sec (θ) - cos (θ)

\frac{sec ( θ )}{tan ( θ )} = csc (θ)

cot (2 b) = \frac{cot ^{2} ( b ) - 1}{2 cot ( b )}

1 + tan^{2} (a) = sec^{2} (a)

Is (1+cos(x))/(sin(x))=cot(x/2) ?
The answer to whether (1+cos(x))/(sin(x))=cot(x/2) is True