Is 2sin(x/2)cos(x/2)=sin(x) ?

The answer to whether 2sin(x/2)cos(x/2)=sin(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove 2sin(x/2)cos(x/2)=sin(x)

prove

2 sin (\frac{x}{2}) cos (\frac{x}{2}) = sin (x)

True

Solution steps

2 sin (\frac{x}{2}) cos (\frac{x}{2}) = sin (x)

Let:

u = \frac{x}{2}

2 sin (u) cos (u) = sin (2 u)

Prove

2 sin (u) cos (u) = sin (2 u) :

True

Therefore

2 sin (\frac{x}{2}) cos (\frac{x}{2}) = sin (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (A) = \frac{cos ( 2 A )}{sin ( A )} + \frac{sin ( 2 A )}{cos ( A )}

sin (θ) csc (θ) + cot (θ) sin (θ) = 1 + cos (θ)

tan (x) cot (x) = csc (x) sec (x)

sin^{2} (θ) = 1 + cos^{2} (θ)

csc (θ) + cos^{2} (θ) = csc (θ)

Is 2sin(x/2)cos(x/2)=sin(x) ?
The answer to whether 2sin(x/2)cos(x/2)=sin(x) is True