The value of the integral `int((1-costheta)^(2/7))/((1+costheta)^(9/7))dthetai s``7/(11)(t a ntheta/2)^((11)/7)+C`(b) `7/(11)(costheta/2)^((11)/7)+C``7/(11)(s intheta/2)^((11)/7)+C`(d)none of theseA. `(7)/(11)("tan"(theta)/(2))^((11)/(7))+C`B. `(7)/(11)("cos"(theta)/(2))^((11)/(7))+C`C. `(7)/(11)("sin"(theta)/(2))^((11)/(7))+C`D. none of these

The value of the integral `int((1-costheta)^(2/7))/((1+costheta)^(9/7)

1.	The value of the integral `int((1-costheta)^(2/7))/((1+costheta)^(9/7))dthetai s``7/(11)(t a ntheta/2)^((11)/7)+C`(b) `7/(11)(costheta/2)^((11)/7)+C``7/(11)(s intheta/2)^((11)/7)+C`(d)none of theseA. `(7)/(11)("tan"(theta)/(2))^((11)/(7))+C`B. `(7)/(11)("cos"(theta)/(2))^((11)/(7))+C`C. `(7)/(11)("sin"(theta)/(2))^((11)/(7))+C`D. none of these
Answer» Correct Answer - A Let `I=int((1-cos theta)^(2//7))/((1+cos theta)^(9//7))d theta` `=int((2sin^(2)theta//2)^(2//7))/((2cos^(2)theta//2)^(9//7))d theta` `=(1)/(2)int((sin theta//2)^(4//7))/((cos theta//2)^(18//7)) d theta` Put `(theta)/(2)=t" or " (d theta)/(2)=dt` ` :. I=int((sint)^(4//7))/((cost)^(18//7)) dt " "("Here, "m+n= -2)` `=int(tant)^(4//7)sec^(2)t dt` Put `tan t=u" or "sec^(2)t dt=du` ` :. I=int u^(4//7)du=(u^(11//7))/(11//7)+c=(7)/(11)(tan t)^(11//7)+C` `=(7)/(11)("tan"(theta)/(2))^(11//7)+C`

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