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

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

Popular >

prove 1-tan^2(x/2)=(2cos(x))/(1+cos(x))

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + cos ( θ )}{1 + sec ( θ )} = cos (θ)

tan^{2} (θ) - sec^{2} (θ) = - 1

cot (x) sin (x) - cos^{2} (x) sec (x) = 0

\frac{cos ( 3 x )}{cos ( x )} = 4 cos^{2} (x) - 3

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

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