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

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

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prove sin(x)=(2tan(x/2))/(1+tan^2(x/2))

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

tan (x) (cot (x) + tan (x)) = sec^{2} (x)

\frac{1 + sin ( 2 x )}{sin ( 2 x )} = 1 + \frac{1}{2} sec (x) csc (x)

(1 - sin^{2} (x)) (1 - sec^{2} (x)) = - sin^{2} (x)

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