Question

cos2a= cos^2 a- sin^2 a for all values of a.
True or False

Answer 1

That looks like an identity.

Answer 2

\[\cos 2a=\cos^2 a-\sin ^2 a\]
Yes, it's an identity.
True

Answer 3

Please prove it @ash2326

Answer 4

We know that
\[\cos (A+B)=\cos A \cos B-\sin A \sin B\]
here
\[A=B=a\]
so
\[\cos (a+a)=\cos a \cos a -\sin a \sin a\]
\[\cos 2a=\cos^2 a-\sin^2 a\]

Answer 5

Further proof (using geometry) can be found here: http://www.themathpage.com/atrig/sum-proof.htm

Answer 6

You can also prove it using complex numbers.