_ /4 ^ /2 , cose c ^ 2 ,d = - Vidyadip

MCQ

$\int_{\pi /4}^{\pi /2} {\cos \theta \,{\rm{cose}}{{\rm{c}}^{\rm{2}}}\theta \,d\theta = } $

✓
$\sqrt 2 - 1$
B
$1 - \sqrt 2 $
C
$\sqrt 2 + 1$
D
None of these

✓

Answer

Correct option: A.

$\sqrt 2 - 1$

a
(a) Let $\int_{\pi /4}^{\pi /2} {\cos \theta \frac{1}{{{{\sin }^2}\theta }}d\theta } $

Put $t = \sin \theta \Rightarrow dt = \cos \theta \,\,d\theta ,$

then we have

$\int_{1/\sqrt 2 }^1 {\frac{1}{{{t^2}}}dt} = \left[ {\frac{{ - 1}}{t}} \right]_{1/\sqrt 2 }^1 $

$= \sqrt 2 - 1$.

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