Question

The integral `int (dx)/(a cos x + b sin x)` is of the form `(1)/(r) " In" [tan ((x + alpha)/(2))]`
What is `alpha` equal to ?
A. `tan^(-1) ((a)/(b))`
B. `tan^(-1) ((b)/(a))`
C. `tan^(-1) ((a + b)/(a -b))`
D. `tan^(-1) ((a -b)/(a +b))`

Answer 1

Correct Answer - A
`a = r sin alpha`..(i)
`b = r cos alpha`...(ii)
Dividing (i) from (ii)
`(a)/(b) = tan alpha`
`alpha = tan^(-1) ((a)/(b))`