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Differentiate tan^(-1) frac((cos x-sin...

Differentiate
`tan^(-1) frac((cos x-sin x))((cos x+ sin x))`

Text Solution

Verified by Experts

`y = tan^(-1)((cos x- sin x)/(cos x + sin x))
= tan^(-1)((1-tan x)/(1+tan x)
= tan^(-1) tan(pi/2-x) = pi/4-x
therefore dy/dx = -1`
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