Question

2 sin theta is equals to X + 1/X and 2 cos theta is equals to X + 1 / X find the value of 2 Sin 3 theta 2 cos 3 theta

Answer 1

2 sinθ=x+1/x......(1),  2 cosθ=x+1/x.........(2)
From (1),(2)
2 sinθ=2 cosθ⇒2 sinθ-2 cosθ=0⇒2(sinθ-cosθ)=0⇒sinθ-cosθ=0⇒sinθ=cosθ
⇒sin³θ=cos³θ
2 cosθ=x+1/x⇒cosθ=(x+1/x)/2=(x²+1)/2 x
2 sin³θ 2 cos³θ=4 sin³θcos³θ=4 [(x²+1)/2 x]³[(x²+1)/2 x]³
=4[(x⁶+1+3 x²+3 x⁴)/8 x³][(x⁶+1+3 x²+3 x⁴)/8 x³]
=(x¹²+6 x¹⁰+15 x⁸+20 x⁶+15 x⁴+6 x²+1)/16 x⁶.....(Ans.)