Double angle for cosine?

Question

I memorized the double angle formula for cos as 1-2sin^2(angle), but a website I'm using is telling me I can use 2cos^2(angle)-1. Is that right?

The example question is:

cos(a) = 2/5 - what is cos(2a)?

Thanks

Answer 1

Both formulas are correct.

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

so 1 - 2sin^2(x) = 2cos^2(x) - 1

cos(2a) = 2cos^2(a) - 1

= 2(2/5)^2 - 1

= 8/25 - 1

= -17/25

Answer 2

cos(a) = 2/5 - what is cos(2a)

cos2a=cos^a-sin^2a

=1-2sin^2a

=2cos^2a-1

=2 (4/5)-1

=8/5-1

=3/5

hint: sin^2a+cos^2a=1

Answer 3

Let Ó¨ = a :-

cos 2Ө = cos ² Ө - sin ² Ө

cos 2Ө = 1 - 2 sin ² Ө

cos 2Ө = 2 cos ² Ө - 1

cos 2Ó¨ = 2 (4/25) - 1

cos 2Ó¨ = 8 / 25 - 1

cos 2Ó¨ = - 17/25