-0-2 x- x-cosec x d x-

The correct option is C π/4Let I=∫_0^π/2sec x/sec x+cosec xdx=∫_0^π/2=sec x ( π/2 x )/sec ( π/2 x )+cosec ( π/2 x )dx =∫_0^π/2 cosec x/cosec x+sec xdx ∴ 2I= ...

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Byju's Answer

Standard XII

Mathematics

Inequalities of Integrals

∫0π/2 x/ x+co...

Question

$\int_{0}^{\frac{π}{2}} \frac{s e c x}{s e c x + c o s e c x} d x =$

\frac{π}{3}

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\frac{π}{2}

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\frac{π}{4}

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\frac{π}{8}

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Solution

The correct option is C $\frac{π}{4}$
$L e t I = \int_{0}^{\frac{π}{2}} \frac{s e c x}{s e c x + c o s e c x} d x = \int_{0}^{\frac{π}{2}} = \frac{s e c x (\frac{π}{2} - x)}{s e c (\frac{π}{2} - x) + c o s e c (\frac{π}{2} - x)} d x$
$= \int_{0}^{\frac{π}{2}} \frac{c o s e c x}{c o s e c x + s e c x} d x$
$∴ 2 I = \int_{0}^{\frac{π}{2}} \frac{s e c x + c o s e c x}{s e c x + c o s e c x} d x = \int_{0}^{\frac{π}{2}} [x]_{0}^{\frac{π}{2}} = \frac{π}{2}$
$∴ I = \frac{π}{4}$

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∫π20sec xsec x+cosec xdx=

The correct option is C π4Let I=∫π20sec xsec x+cosec xdx=∫π20=sec x(π2−x)sec(π2−x)+cosec(π2−x)dx =∫π20 cosec xcosec x+sec xdx ∴2I=∫π20sec x+cosec xsec x+cosec xdx=∫π20[x]π20=π2 ∴ I=π4

$\int_{0}^{\frac{π}{2}} \frac{s e c x}{s e c x + c o s e c x} d x =$