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

The integral `int (dx)/(a cos x + b sin x)` is of the form `(1)/(r) "

1.	The integral `int (dx)/(a cos x + b sin x)` is of the form `(1)/(r) " In" [tan ((x + alpha)/(2))]` What is r equal to ?A. `a^(2) + b^(2)`B. `sqrt(a^(2) + b^(2))`C. `a + b`D. `sqrt(a^(2) + b^(2))`
Answer» Correct Answer - B Given that, `int (dx)/(a cos x + b sin x) = (1)/(r) ln [tan ((x + alpha)/(2))]` Let `a = r sin alpha, b = r cos alpha` `int (dx)/(r sin alpha cos x + r cos alpha sin x) = (1)/(r) int (1)/(sin (x + alpha))` `= (1)/(r) int "cosec"(x + alpha) dx = (1)/(r) ln [tan((x + alpha)/(2))]` `a = r sin alpha rArr a^(2) = r^(2) sin^(2) alpha`...(i) `b = r cos alpha rArr b^(2) = r^(2) cos^(2) alpha`...(ii) Adding (i) and (ii), we get `r^(2) = a^(2) + b^(2)` `rArr r= sqrt(a^(2) + b^(2))`

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