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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Factor

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

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

Rewrite using trig identities

= cos^{3} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (x + \frac{3 π}{2}) = sin (x)

1 - tan^{4} (A) = 2 sec^{2} (A) - sec^{4} (A)

cos^{4} (θ) - sin^{4} (θ) = 2 cos^{2} (θ) - 1

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

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