Prove that `cos ^(-1) x = 2 sin ^(-1).sqrt(1-x)/(2)`

1.	Prove that `cos ^(-1) x = 2 sin ^(-1).sqrt(1-x)/(2)`
Answer» Let `cos^(-1) x = theta` `rArr" "x - cos theta` R.H.S `= 2 sin sqrt((1-x)/(2)) = 2sin. sqrt((1-costheta))/(2)` `= 2 sin ^(-1).sqrt((2 sin^(2)((theta)/(2)))/(2)) = 2 sin (sin.(theta)/(2)`) ` 2.(theta)/(2)= theta= cos^(-1) x= L.H.S`

Discussion

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