Question

rove the identiy of cos 2u=2 cos^2u-1

Answer 1

So we have cos 2u = Cos(U + U)

If U = A, U = B

Then cos(A+B) = cosAcosB - sinAsinB (known identity)

= cos U. cos U - sin U.sinU

=> cos2U - sin2U

=> cos2U - (1 - cos2U) (sin2U + cos2U = 1)

=> 2cos2U - 1 = cos 2U. proved.