If 2 cos theta = x + 1/x, prove that 2 cos 3 theta = x cube + 1/x cube - Maths - Trigonometric Functions

Question

If 2 cos theta = x + 1/x, prove that 2 cos 3 theta = x cube + 1/x
cube

Manbar Singh · Accepted Answer

We have,    2 cos θ = x + 1xcubing both sides, we get     2 cos θ3 =  x + 1x3⇒8 cos3θ = x3 + 1x3 + 3 × x × 1xx + 1x⇒8 cos3θ =  x3 + 1x3 + 3 2 cos θ⇒8 cos3θ - 6 cos θ =  x3 + 1x3=24 cos3θ - 3 cos θ = x3 + 1x3⇒2 cos 3θ = x3 + 1x3

Hence, we can say that : 2cosnθ=xn+1xn

If 2 cos theta = x + 1/x, prove that 2 cos 3 theta = x cube + 1/x cube.