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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

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

sin (x) sin (x) = tan (x)

cot (a) sin (a) = cos (a)

\frac{sec ( x ) - csc ( x )}{cot ( x ) - 1} = cos (x)

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

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