Is tan(θ/2)=(sin(θ))/(1+cos(θ)) ?

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

Popular >

prove tan(θ/2)=(sin(θ))/(1+cos(θ))

prove

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

True

Solution steps

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

Let:

u = \frac{θ}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cot (t) cos (t) = csc (t) - sin (t)

sin (\frac{3 π}{2} - x) = - cos (x)

sin (x) sec (x) = \frac{1}{cot ( x )}

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

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

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