+956 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...
+128460
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
