Is (1-cos(x))/(1+cos(x))=tan^2(x/2) ?

The answer to whether (1-cos(x))/(1+cos(x))=tan^2(x/2) is True

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prove (1-cos(x))/(1+cos(x))=tan^2(x/2)

prove

\frac{1 - cos ( x )}{1 + cos ( x )} = tan^{2} (\frac{x}{2})

True

Solution steps

\frac{1 - cos ( x )}{1 + cos ( x )} = tan^{2} (\frac{x}{2})

Let:

u = \frac{x}{2}

\frac{1 - cos ( 2 u )}{1 + cos ( 2 u )} = tan^{2} (u)

Prove

\frac{1 - cos ( 2 u )}{1 + cos ( 2 u )} = tan^{2} (u) :

True

Therefore

\frac{1 - cos ( x )}{1 + cos ( x )} = tan^{2} (\frac{x}{2})

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{π}{3}) = \frac{3}{2}

\frac{tan ( x )}{1 - cos ( x )} = csc (1 + sec (x))

cos (t) sec (\frac{π}{2} - t) = cot (t)

\frac{( 1 - cos ( 2 x ) )}{sin ( 2 x )} = tan (x)

cot^{2} (α) = cos^{2} (α) + (cot (α) cos (α))^{2}

Is (1-cos(x))/(1+cos(x))=tan^2(x/2) ?
The answer to whether (1-cos(x))/(1+cos(x))=tan^2(x/2) is True