Question

If 2 cos ø = x +1/x
prove that 2 cos 3ø = x³ +1/x³


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Answer 1

Answer:

Step-by-step explanation:

x + 1/x = 2 cosA.

We know that a^3+b^3 = (a+b)^3–3ab(a+b)

So (x^3 + 1/x^3)=(x + 1/x)^3 -3×x×(1/x)(x + 1/x)

= (2cosA)^3 - 3×2cosA = 8cos^3A - 6cosA

= 2(4cos^3A - 3cosA) = 2cos3A . (Since cos3A = 4cos^3A-3cosA).