Question

Solve the equation 2cos^2x = sin2x , giving your answer in terms of π. 0 14 years ago

Answer 1

use double angle formula for the right side to get:
2cos^2x = 2sinxcosx
2cos^2x - 2sinxcosx = 0
2cosx(cosx - sinx) = 0

so cosx = 0 gives pi/2.
cosx - sinx = 0 or tanx = 1 gives pi/4.

Answer 2

can i try this way?
2cos^2x = sin2x
cos2x +1 = sin2x
cos2x - sin2x =-1
(cos2x - sin2x)^1 = (-1)^2
(cos2x)^2 -2cos2xsin2x + (sin2x)^2 =1
1-2sin2xcos2x =1
-sin4x = 0
sin4x =0
4x = π
x = π/4

Answer 3

Thanks a lot!

Answer 4

np