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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`
Solution
`"tan"^-1 (("cos x - sin x")/("cos x + sin x"))`
`Rightarrow "tan"^-1 ((1 - "sin x"/"cos x")/(1 + "sin x"/"cos x"))`
`Rightarrow "tan"^-1 ((1 - "tan x")/(1 + "tan x"))`
`Rightarrow "tan"^-1 (1) - "tan"^-1 ("tan x")`
`Rightarrow pi/4 - "x"`
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