यदि (If) `y=tan^(-1)sqrt((1+sinx)/(1-sinx)),` (find) `(dy)/(dx)` ज्ञात करें।

Explanation

`y=tan^(-1)sqrt((1+sinx)/(1-sinx))=tan^(-1)sqrt(("cos"^(2)(x)/(2)+"sin"^(2)(x)/(2)+2" sin"(x)/(2) "cos"(x)/(2))/("cos"^(2)(x)/(2)+"sin"^(2)(x)/(2)-2"sin"(x)/(2)"cos"(x)/(2)))`
`=tan^(-1)sqrt((("cos"(x)/(2)+"sin"(x)/(2))^(2))/(("cos"(x)/(2)-"sin"(x)/(2))^(2)))`
`=tan^(-1)(("cos"(x)/(2)+"sin"(x)/(2))/("cos"(x)/(2)-"sin"(x)/(2)))=tan^(-1)((1+"tan"(x)/(2))/(1-"tan"(x)/(2)))`
`thereforey=tan^(-1)[tan((pi)/(4)+(x)/(2))]=(pi)/(4)+(x)/(2)rArr(dy)/(dx)=(1)/(2)`