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Q.

$\int_{π / 4}^{π / 2} \cos θ {cosec}^{2} θ d θ = ?$

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a

None of these

b

$\sqrt{2} - 1$

c

$1 - \sqrt{2}$

d

$\sqrt{2} + 1$

answer is A.

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Detailed Solution

Let $\int_{π / 4}^{π / 2} \cos θ \frac{1}{\sin^{2} θ} d θ$

Put $t = \sin θ \Rightarrow d t = \cos θ d θ$ , then we have

$\int_{1 / \sqrt{2}}^{1} \frac{1}{t^{2}} d t = [{\frac{- 1}{t}|}_{1 / \sqrt{2}}^{1} = \sqrt{2} - 1 .$

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∫π/4π/2 cos⁡θcosec2⁡θdθ=?