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Express in the simplest form tan^(-1) ((...

Express in the simplest form `tan^(-1) ((cos x-sinx)/(cosx+sin x))`

Text Solution

Verified by Experts

`(cosx-sinx)/(cosx+sinx)=(1-tanx)/(1+tanx)`
`tan(A-B)=(tanA-tanB)/(1+tanAtanB)`
`=tan(pi/4-x)`
putting this value in question.
`tan^(-1)tan(pi/4-x)`
`pi/4-x`.
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