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If x<0 , then write the value of cos^...

If `x<0` , then write the value of `cos^(-1)((1-x^2)/(1+x^2))` in terms of `tan^(-1)x`

Text Solution

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Let `x=tany`
`cos^(-1)((1-tan^2y)/(1+tan^2y))`
`frac{1-tan^2x}{1+tan^2x}=cos2x`
`cos^(-1)cos 2y=>2y`
x is negative
Let `x=-a` where `a>0`
`tany=-a=>y=tan^(-1)(-a)`
`y=tan^(-1)x` ...
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