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

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

Popular >

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

prove

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

True

Solution steps

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

Let:

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

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) - 2 cos^{2} (x) = 1 - 3 cos^{2} (x)

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

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

cos (θ - \frac{π}{2}) = sin (θ)

csc (x) \cdot cos (x) = cot (x)

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