Question -
Answer -
Let us consider LHS:
1 + cos2 2x
We know, cos2x = cos2 x – sin2 x
cos2 x + sin2 x = 1
so,
1 + cos2 2x = (cos2 x+ sin2 x) 2 + (cos2 x –sin2 x) 2
= (cos4 x + sin4 x + 2cos2 x sin2 x) + (cos4 x + sin4 x– 2 cos2 x sin2 x)
= cos4 x + sin4 x +cos4 x + sin4 x
= 2 cos4 x + 2 sin4 x
= 2 (cos4 x + sin4 x)
= RHS
Hence proved.