Question

if 2 cos theta=x+1/x prove that 2 cos 3theta=x^3+1/x^3​

Answer 1

Answer:

Step-by-step explanation:

Formula:

a3+b3=(a+b)3−3ab(a+b)

Given that,

2cosθ=x+x1​

⟹cosθ=21​(x+x1​)

2cos3θ=2(4cos3θ−3cosθ)=8cos3θ−6 cosθ

=8.81​(x+x1​)3−6.21​(x+x1​)

=(x+x1​)3−3(x+x1​)

=(x+x1​)3−3.x.x1​(x+x1​)

=x3+x31​