Question

prove that sin 4 theta + cos 4 theta minus is equal to 1 minus 2 sin square theta into cos square theta

Answer 1

sin4θ+cos4θ=(sin4θ+2sin2θcos2θ+cos4θ)−2sin2θcos2θsin4⁡θ+cos4⁡θ=(sin4⁡θ+2sin2⁡θcos2⁡θ+cos4⁡θ)−2sin2⁡θcos2⁡θ

=(sin2θ+cos2θ)2−2sin2θcos2θ=(sin2⁡θ+cos2⁡θ)2−2sin2⁡θcos2⁡θ