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

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

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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

tan (x) csc^{2} (x) - tan (x) = cot (x)

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

sin (θ) + cos (θ) cot (θ) = csc (θ)

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

sin (x - \frac{π}{6}) + cos (x) = sin (x + \frac{π}{6})

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