Is sin(3θ)=3cos^2(θ)sin(θ)-sin^3(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (3 θ)

Rewrite using trig identities

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

Expand

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( θ ) cos ( θ )}{sin ( θ )} = 1

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

sec (x) - cos (x) = sin (x) (tan (x))

sin (x) sin (3 x) = 4 sin (x) cos^{2} (x)

sec (\frac{π}{2} - t) = csc (t)

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