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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= cos^{4} (a)

We showed that the two sides could take the same form

\Rightarrow True

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