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

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

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

prove

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

True

Solution steps

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

Let:

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

We showed that the two sides could take the same form

\Rightarrow True

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

sin (3 x) cos (2 x) - cos (3 x) sin (2 x) = sin (x)

4 cot^{2} (y) (sec^{2} (y) - 1) = 4

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

sin^{2} (x) sec (x) = \frac{sin ( x )}{cot ( x )}

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