What two common identities are most useful for proving that 2cos^2x = cos2x+1

I went off starting that cos2x is an identity but stuff wasn't working out...

Julius
Dec 5, 2017

#1**+3 **

One thing about these identities is that there may be more than one way of proving them

So...let's try this....

2cos^2 (x) = cos(2x) +1

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

2 - 2sin^2 (x) = cos(x)cos(x) - sin(x)sin(x) + 1 subtract 1 from both sides

1 - 2sin^2(x) = cos^2(x) - sin^2(x) add 2 sin^2x to both sides

1 = cos^2(x) + sin^2(x) which is true

CPhill
Dec 5, 2017