Question

cos^2 2A+4sin^2A×cos^2 A=1

Answer 1

Using Sin^2 and Cos^2 identities,
= Cos^2(2A) + 4[(1/2)(1-Cos(2A)][(1/2)(1+Cos(2A)] = 1
= Cos^2(2A) + 1 -Cos^2(2A) = 1
   0 = 0
There is nothing to solve for as it is an identity of sorts.