If 2Cosθ = x+1/x So, Prove That ? Cos2θ = 1/2(x²+1/x²)

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If 2Cosθ = x+1/x So, Prove That ? Cos2θ = 1/2(x²+1/x²)

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Answer 1 · 2018-05-20T15:50:36

$LHS=cos2theta$

$=2cos^2theta-1$

$=2(1/2(x+1/x))^2-1$

$=1/2(x^2+1/x^2+2*x*1/x)-1$

$=1/2(x^2+1/x^2)+1/2*2-1$

$=1/2(x^2+1/x^2)=RHS$

Answer 2 · 2018-05-20T16:13:10

Sqaring the given equation we get
$cos(theta)=1/4*(x^2+1/x^2+2)$ then by multiplying by $2$ we get
$2cos^2(theta)=1/2*(x^2+1/x^2)+1$ from here we get
$2cos^2(theta)-1=1/2(x^2+1/x^2)$

Explanation:

we used $(x+1/x)^2=x^2+1/x^2+2$
$cos(2x)=2cos^2(x)-1$

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If 2Cosθ = x+1/x So, Prove That ? Cos2θ = 1/2(x²+1/x²)

2 Answers

Explanation:

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