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

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

Grade:12

1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 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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