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What is the Intregration of 1/sin x + cos x dx ?

What is the Intregration of  1/sin x + cos x  dx  ?

Grade:12

1 Answers

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

I = \int \frac{dx}{sinx+cosx}
I = \frac{1}{\sqrt{2}}\int \frac{dx}{sinx.\frac{1}{\sqrt{2}}+cosx.\frac{1}{\sqrt{2}}}
sin(x+\frac{\pi }{4}) = sinx.cos\frac{\pi }{4}+cosx.sin\frac{\pi }{4}
I = \frac{1}{\sqrt{2}}\int \frac{dx}{sin(x+\frac{\pi }{4})}
I = \frac{1}{\sqrt{2}}\int cosec(x+\frac{\pi }{4})dx
I = \frac{1}{\sqrt{2}}log(\frac{x+\frac{\pi }{4}}{2}) + c

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