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evaluate the following integral ∫ sin 2x / sin(x – pi/6) sin(x + pi/6) dx

evaluate the following integral
∫ sin 2x / sin(x – pi/6) sin(x + pi/6) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello student,
Please find the answer to your question below

I = \int \frac{sin2x}{sin(x-\frac{\pi }{6})sin(x+\frac{\pi }{6})}dx
I = \int \frac{sin(x+\frac{\pi }{6}+x-\frac{\pi }{6})}{sin(x-\frac{\pi }{6})sin(x+\frac{\pi }{6})}dx
I = \int \frac{sin(x+\frac{\pi }{6})cos(x-\frac{\pi }{6})+cos(x+\frac{\pi }{6})sin(x-\frac{\pi }{6})}{sin(x-\frac{\pi }{6})sin(x+\frac{\pi }{6})}dx
I = \int \frac{cos(x-\frac{\pi }{6})}{sin(x-\frac{\pi }{6})}dx+\int \frac{cos(x+\frac{\pi }{6})}{sin(x+\frac{\pi }{6})}dx
I = log(sin(x-\frac{\pi }{6}))+log(sin(x+\frac{\pi }{6}))+c

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