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evaluate the following integral ∫ cos x / cos(x – a) dx

evaluate the following integral
∫ cos x / cos(x – a) dx

Grade:12

1 Answers

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

I = \int \frac{cosx}{cos(x-a)}dx
I = \int \frac{cos(x-a+a)}{cos(x-a)}dx
I = \int \frac{cos(x-a)sina+sin(x-a)cosa}{cos(x-a)}dx
I = \int sinadx+\int \frac{sin(x-a)cosa}{cos(x-a)}dx
I = (sina)x+cosa\int \frac{sin(x-a)}{cos(x-a)}dx
cos(x-a) = t
-sin(x-a)dx = dt
I = (sina)x+cosa\int \frac{-dt}{t}
I = (sina)x-cosa lnt+c
I = (sina)x-cosa ln(cos(x-a))+c

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