Question

prove it and post complete solution.
pls

Answer 1

Given 1 + cos^2 2 theta 

We know that cos 2 theta = cos^2 theta - sin^2 theta

 = 1 + (cos^2 theta - sin^2 theta)^2

 It is in the form of (a - b)^2

= 1 + cos^4 theta + sin^4 theta - 2 sin^2 theta cos^2 theta

= sin^2 theta + cos^2 theta + cos^4 theta + sin^4 theta - 2 sin^2 theta cos^2 theta

= sin^2 theta(1-cos^2 theta) + cos^2 theta(1-sin^2 theta) + cos^4 theta + sin^4 theta

= sin^2 theta * sin^2 theta + cos^2 theta * cos^2 theta + cos^4 theta + sin^4 theta

= sin^4 theta + cos^4 theta + cos^4 theta + sin^4 theta

= 2(cos^4 theta + sin^4 theta).

LHS = RHS.


Hope this helps!