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

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

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

prove

sin (4 a) = 2 sin (2 a) cos (2 a)

True

Solution steps

sin (4 a) = 2 sin (2 a) cos (2 a)

Manipulating right side

2 sin (2 a) cos (2 a)

Rewrite using trig identities

2 sin (2 a) cos (2 a)

Use the Double Angle identity:

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

= sin (2 \cdot 2 a)

Simplify

= sin (4 a)

= sin (4 a)

We showed that the two sides could take the same form

\Rightarrow True

tan (x) = sec (x) sin (x)

sin (2 D) = 2 cot (D) sin^{2} (D)

tan^{2} (\frac{π}{6}) = \frac{1}{3}

\frac{1 + csc ^{2} ( x )}{csc ^{2} ( x )} = 1 + sin^{2} (x)

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

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