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If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2...

If `y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)),` then find= `(dy)/(dx)`

Text Solution

Verified by Experts

The correct Answer is:
`(-2)/(sqrt(1-x^(2)))`
`y=sec^(-1)((1)/(2x^(2)-1)),0ltxlt(1)/(sqrt(2))`
Let `x= cos theta.` Therefore,
`y=sec^(-1)((1)/(2cos^(2)theta-1))`
`sec^(-1)((1)/(cos 2 theta))`
`=sec^(-1)(sec 2theta)`
`2theta`
`=2 cos^(-1)x`
`rArr" "(dy)/(dx)=(-2)/(sqrt(1-x^(2))`
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