Question

`int_0^{pi/2} (cos2x)/(cosx + sinx)dx` = ______

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Answer 1

`int_0^{pi/2} (cos2x)/(cosx + sinx)dx` = 0

Explanation:

`int_0^{pi/2} (cos2x)/(cosx + sinx)dx`

= `int_0^{pi/2} (cos^2x - sin^2x)/(cosx + sinx)dx`

= `int_0^{pi/2} (cosx - sinx)dx`

= `[sinx + cosx]_0^{pi"/"2} = 0`