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y=sec^(-1)""(1)/(2x^(2)-1),0ltxlt(1)/(sq...

`y=sec^(-1)""(1)/(2x^(2)-1),0ltxlt(1)/(sqrt(2))`

Text Solution

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`y = sec^(-1)((1)/(2x^(2) -1 ))`
Let x = cos theta
`rArr theta cos ^(-1) x `
`rArr y sec ^(-1)((1)/(2 cos^(2)theta-1))`
`= sec^(-1)((1)/(cos2 theta))`
= `sec^(-1)(sec2 theta)`
`= 2theta = 2 cos ^(-1)x `
`rArr (dy)/(dx)=2(d)/(dx) cos ^(-1)x = - (2)/(sqrt(1 - x ^(2)))`
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