Prove that Cos^-1(2x²-1) = 2Cos^-1(x)
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Step-by-step explanation:
cos -1 (2x2 – 1) = 2 cos -1 x
Take x = cos θ
Where θ = cos -1 x
Here LHS = cos -1 (2x2 – 1)
By substituting the value of x
= cos -1 (2cos2 θ – 1)
It can be written as
= cos -1 (cos 2 θ)
= 2 θ
Substituting the value of θ
= 2 cos -1 x
= RHS
Hence, it is proved.
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Answer:
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