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Question
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
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Solution
Let y = `tan^-1 ((cos x + sin x)/(cos x - sin x))`
y = `tan^-1 ((cos x(1 + (sinx)/(cosx)))/(cos x(1 - (sin x)/(cos x))))`
y = `tan^-1 ((1 + tanx)/(1 - tanx))`
= `tan^-1 ((tan pi/4 + tan x)/(1 - tan pi/4 * tan x))`
= `tan^-1 (tan (pi/4 + x))`
y = `pi/4 + x`
`("d"y)/("d"x)` = 0 + 1
`("d"y)/("d"x)` = 1
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