Is sin(3x)=3cos^2(x)sin(x)-sin^3(x) ?

The answer to whether sin(3x)=3cos^2(x)sin(x)-sin^3(x) is True

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prove sin(3x)=3cos^2(x)sin(x)-sin^3(x)

prove

sin (3 x) = 3 cos^{2} (x) sin (x) - sin^{3} (x)

True

Solution steps

sin (3 x) = 3 cos^{2} (x) sin (x) - sin^{3} (x)

Manipulating left side

sin (3 x)

Rewrite using trig identities

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

Expand

(cos^{2} (x) - sin^{2} (x)) sin (x) + 2 cos (x) cos (x) sin (x) : - sin^{3} (x) + 3 cos^{2} (x) sin (x)

= - sin^{3} (x) + 3 cos^{2} (x) sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (3 x) + cos (x) = 4 cos^{3} (x) - 2 cos (x)

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

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

cos (2 x) - 3 sin^{2} (x) = 1 - 5 sin^{2} (x)

Is sin(3x)=3cos^2(x)sin(x)-sin^3(x) ?
The answer to whether sin(3x)=3cos^2(x)sin(x)-sin^3(x) is True