Question

`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.

विकल्प

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Answer 1

`int_0^(pi/2) 1/(1 + cosx) "d"x` = 1.

Explanation:

`int_0^(pi/2) 1/(1 + cosx) "d"x = int_0^(p/2) 1/(2cos^2(x/2)) "d"x`

= `1/2 int_0^(pi/2) sec^2(x/2)"d"x`

= `1/2[(tan(x/2))/(1/2)]_0^(pi/2)`

= `tan  pi/4 - tan 0`

= 1