Is sin(3a)+sin(a)=4sin(a)-4sin^3(a) ?

The answer to whether sin(3a)+sin(a)=4sin(a)-4sin^3(a) is True

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prove sin(3a)+sin(a)=4sin(a)-4sin^3(a)

prove

sin (3 a) + sin (a) = 4 sin (a) - 4 sin^{3} (a)

True

Solution steps

sin (3 a) + sin (a) = 4 sin (a) - 4 sin^{3} (a)

Manipulating left side

sin (3 a) + sin (a)

Rewrite using trig identities

= 4 sin (a) - 4 sin^{3} (a)

We showed that the two sides could take the same form

\Rightarrow True

sin (2 t) = 2 sin (t) (cos (t))

2 sin (x + 4 5^{\circ}) = sin (x) + cos (x)

4 cot (θ) = cot (θ) sin^{2} (θ)

cos (2 θ) + 1 = 2 cos^{2} (θ)

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

Is sin(3a)+sin(a)=4sin(a)-4sin^3(a) ?
The answer to whether sin(3a)+sin(a)=4sin(a)-4sin^3(a) is True