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

abhilash , 10 Years ago
Grade 12
anser 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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