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Question
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
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Solution
`tan^-1 ((cos x - sin x)/(cos x + sin x))`
= `tan^-1 ((1 - sin x/cos x)/(1 + sin x/cos x))`
= `tan^-1 ((1 - tan x)/(1 + tan x))`
= tan−1 (1) − tan−1 (tan x)
= `pi/4 - x`
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