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Integral Calculus> Integrate sqrt sin(x-a)/sqrt sin(x+a)...

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Integrate sqrt sin(x-a)/sqrt sin(x+a)

abhilash , 10 Years ago

Grade 12

1 Answers

Latika Leekha

Last Activity: 10 Years ago

Hello student,
The given question is $\int \sqrt{\frac{sin(x-a)}{sin(x+a)}}dx$
Let I = $\int \sqrt{\frac{sin(x-a)}{sin(x+a)}}dx$
= $\int {\frac{sin(x-a)}\sqrt{sin(x+a)sin(x-a)}}dx$
= $\int \frac{sinx cos a-cos xsina}\sqrt{sin^{2}x-sin^{2}a}$
= I₁ – I₂
Now, we have

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