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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Factor

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

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

Rewrite using trig identities

= sin^{3} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cot (u) tan (u) - cos^{2} (u) = sin^{2} (u)

\frac{csc ^{4} ( x ) - 1}{cot ^{2} ( x )} = csc^{2} (x) + 1

\frac{1}{csc ( x )} = sin (x)

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

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