Is cos^2(x)-cos^4(x)=cos^2(x)sin^2(x) ?

The answer to whether cos^2(x)-cos^4(x)=cos^2(x)sin^2(x) is True

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prove cos^2(x)-cos^4(x)=cos^2(x)sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (x) - cos^{4} (x)

Factor

cos^{2} (x) - cos^{4} (x) : cos^{2} (x) (1 - cos^{2} (x))

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

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sin ( θ )} - sin (θ) = cot (θ) cos (θ)

sin (θ) cos (θ) (tan (θ) + cot (θ)) = 1

tan (x) = \frac{sec ( x )}{csc ( x )}

\frac{csc ( θ )}{cot ( θ )} = sec (θ)

\frac{sin ( t )}{1 - cos ( t )} = csc (t) + cot (t)

Is cos^2(x)-cos^4(x)=cos^2(x)sin^2(x) ?
The answer to whether cos^2(x)-cos^4(x)=cos^2(x)sin^2(x) is True