Question

2cos y=x+1/x, Prove that cos 2y=1/2(x^2+1/x^2)


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Answer 1

Answer is in the attachment

Answer 2

Answer:

We're given that 2cos y=x+1/x. Now, we have to prove that cos 2y=1/2(x^2+1/x^2).

Let's see the proof.

cos 2y = 2 cos²y - 1

= 2 × [ 1/2 × (x + 1/x)² - 1 ]

= 1/2 × (x + 1/x)² - 1

= 1/2 × ( x² + 2 + 1/x² ) - 1

= 1/2 (x² + 1/x²)

Hence, proved.

Thus, cos 2y = 1/2 (x² + 1/x²).