`inttan^(-1)sqrt((1-sinx)/(1+sinx))dx`का मान ज्ञात कीजिए।

Explanation

हम जानते है
`(1-sinx)/(1+sinx) = (cos^(2) .(x)/(2)+ sin^(2).(x)/(2)-2cos.(x)/(2)sin.(x)/(2))/(cos^(2).(x)/(2)+sin^(2).(x)/(2)+ 2cos.(x)/(2)sin.(x)/(2))`
`((cos.(x)/(2) - sin.(x)/(2))/(cos.(x)/(2)+sin.(x)/(2)))`
`rArr sqrt((1-sinx)/(1+sinx))=(cos.(x)/(2)-sin.(x)/(2))/(cos.(x)/(2)+sin.(x)/(2))`
` = (1-(sin x//2)/(cos x//2))/(1+(sin//2)/(cosx//2)) = (1-tan.(x)/(2))/(1+tan.(x)/(2))= tan((pi)/(2) - (x)/(2))`
`therefore int tan^(-1) sqrt((1-sinx)/(1+sin))dx = int tan^(-1) [ tan ((pi)/(4) - (pi)/(2))]dx`
` = int ((pi)/(4) - (x)/(2))dx = (pi)/(4)x - (x^2)/(4) + c`