`tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)-(1)/(2)cos^(-1)x,-(1)/(sqrt2)lexle1`

`tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)-(1)/(2

1.	`tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)-(1)/(2)cos^(-1)x,-(1)/(sqrt2)lexle1`
Answer» माना `x=costhetaimpliestheta=cos^(-1)x` `L.H.S.=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))` `=tan^(-1)((sqrt(1+costheta)-sqrt(1-costheta))/(sqrt1+costheta+sqrt(1-costheta)))` `=tan^(-1)""(sqrt(2cos^(2)""(theta)/2)-sqrt(2sin^(2)""(theta)/(2)))/(sqrt(2cos^(2)""(theta)/(2))+sqrt(2sin^(2)""(theta)/(2)))` `=tan^(-1)((cos""(theta)/(2)-sin""(theta)/(2))/(cos""(theta)/(2)+sin""(theta)/(2)))` `=tan^(-1)((1-tan""(theta)/(2))/(1+tan""(theta)/(2)))` `=tan^(-1)tan((pi)/(4)-(theta)/(2))=(pi)/(4)-(theta)/(2)` `=(pi)/(4)-(1)/(2)cos^(-1)x=R.H.S.`

निम्नलिखित के मुख्य मानो को ज्ञात कीजिए : `cot^(-1)(sqrt(3))`
यदि `cot^(-1)(sqrt(cos alpha ))- tan^(-1)(sqrt(cos alpha))=x` तब `sin x=`A. `tan^(1)""(alpha)/(2)`B. `tan alpha `C. `cot^(2)""(alpha)/(2)`D. `cot alpha `
निम्नलिखित के मुख्य मानो को ज्ञात कीजिए : ` sin^(-1)""((-1)/(2))`
सरलतम रूप में लिखिए - `cot^(-1)((1)/(sqrt(x^(2)-1))), |x| gt1`
सरलतम रूप व्यक्त कीजिए - `tan^(-1)((cosx)/(1-sinx))`
`tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2))),agt0 , = (a)/(sqrt(3)) lt x lt (a)/(sqrt(3))` को सरलतम रूप में लिखे |
`tan^(-1)""(1)/(sqrt(x^(2)-1)),|x|gt1`
`tan^(-1)""((sqrt(1-cosx))/(1+cosx)),0ltxltpi`
`tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lta` को सरलतम रूप में लिखे |
`tan^(-1)((cosx - sinx)/(cosx + sinx)), - (pi)/(4)ltxlt(3pi)/(4)` को सरलतम रूप में लिखे |