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Question
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
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Solution
`int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx = int_(-π//4)^(π//4) (2 cos^2 x - 1)/(2 cos^2 x)dx`
= `1/2 . 2 int_0^(π//4) (2 - sec^2 x)dx` ...[even function]
= `1/2 . 2[2x - tan x]_0^(π//4)`
= `π/2 - 1`
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