Is sin(4x)=2sin(2x)cos(2x) ?

The answer to whether sin(4x)=2sin(2x)cos(2x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove sin(4x)=2sin(2x)cos(2x)

prove

sin (4 x) = 2 sin (2 x) cos (2 x)

True

Solution steps

sin (4 x) = 2 sin (2 x) cos (2 x)

Manipulating right side

2 sin (2 x) cos (2 x)

Rewrite using trig identities

2 sin (2 x) cos (2 x)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 \cdot 2 x)

Simplify

= sin (4 x)

= sin (4 x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e \frac{cos ( x ) cot ( x )}{1 - sin ( x )} - 1 = csc (x)

p ro v e (1 + tan (x))^{2} = sec^{2} (x) + 2 tan (x)

p ro v e \frac{sec ^{2} ( x )}{2 tan ( x )} = csc (2 x)

p ro v e (sec^{2} (x) - 1) csc (x) = tan (x) sec (x)

p ro v e cos (x - \frac{π}{2}) = sin (x)

Is sin(4x)=2sin(2x)cos(2x) ?
The answer to whether sin(4x)=2sin(2x)cos(2x) is True