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If 2costheta=x+1/x, then 2cos2theta=?...

If `2costheta=x+1/x`, then `2cos2theta=`?

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i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x) , then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

If 2 cos theta=x+1/x then prove that cos 2 theta=1/2 (x^(2)+1/x^(2))