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

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

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

prove

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

True

Solution steps

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

Let:

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

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) = sin (θ - 2 π)

3 sec^{2} (x) - 2 tan^{2} (x) - 4 = 0

tan (θ) cot (θ) - 1 = 1 - sec (θ) cos (θ)

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

(tan (θ) + 1) (tan (θ) - 1) = sec^{2} (θ) - 2

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