if cos theta + cos^2 = 1 then prove that sin^12 + 3 sin^10 +3 sin^8 + sin^6 + 2 - Maths - Introduction to Trigonometry

Question

if cos theta + cos^2 = 1 then prove that sin^12 + 3 sin^10 +3 sin^8
+ sin^6 + 2 sin^4 +2 sin^2 = 1

Rishabh Mittal · Accepted Answer

Assuming question isTo Prove:-sin12θ+3 sin10θ+3 sin8θ+sin6θ+2 sin4θ+2 sin2θ=3cos θ+cos2θ=1cos θ=1-cos2θcos θ=sin2θLHS = sin12θ+3 sin10θ+3 sin8θ+sin6θ+2 sin4θ+2 sin2θ     =sin4θ3+3sin4θ2sin2θ+3sin4θsin2θ2+sin2θ3+2sin4θ+sin2θ=sin4θ+sin2θ3+2sin4θ+sin2θ     Since a+b3=a3+3a2b+3ab2+b3=cos2θ+sin2θ3+2cos2θ+sin2θ     Since cos θ=sin2θ=1+2=3=RHSHence Proved

if cos theta + cos^2 = 1 then prove that sin^12 + 3 sin^10 +3 sin^8 + sin^6 + 2 sin^4 +2 sin^2 = 1