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Find the value of tan^(-1)(-x)-cot^(-1)(...

Find the value of `tan^(-1)(-x)-cot^(-1)(-1/x),x gt0`

Text Solution

Verified by Experts

Since, `tan^(-1)(-x)=-tan^(-1)x`
`and cot^(-1)(-1/x)=pi-cot^(-1)1/x`
Also, `cot^(-1)(-1/x)=tan^(-1)x,x gt 0`
`:.tan^(-1)(-x)-cot^(-1)(-1/x)`
`-tan^(-1)x-(pi-cot^(-1)1/x)`
`=-tan^(-1)x-pi+tan^(-1)x`
`=-pi`
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