The derivative of `cos(2tan^(-1)sqrt((1-x)/(1+x)))-2cos^(-1)sqrt((1-x)/(2))` w.r.t. x isA. `1-(1)/(sqrt(1-x^(2)))`B. `1-(1)/(sqrt(1+x^(2)))`C. `2-(1)/(sqrt(1-x^(2)))`D. `2-(1)/(sqrt(1+x^(2)))`

The derivative of `cos(2tan^(-1)sqrt((1-x)/(1+x)))-2cos^(-1)sqrt((1-x)

1.	The derivative of `cos(2tan^(-1)sqrt((1-x)/(1+x)))-2cos^(-1)sqrt((1-x)/(2))` w.r.t. x isA. `1-(1)/(sqrt(1-x^(2)))`B. `1-(1)/(sqrt(1+x^(2)))`C. `2-(1)/(sqrt(1-x^(2)))`D. `2-(1)/(sqrt(1+x^(2)))`
Answer» Correct Answer - A Let `x=cos theta, therefore theta=cos^(-1)x` `therefore" "y=cos (2 tan^(-1)sqrt((1-x)/(1+x)))-2cos^(-1).sqrt((1-x)/(2))` `=cos(2tan^(-1)(tan.(theta)/(2)))-2 cso^(-1)(sin.(theta)/(2))` `=cos theta-2((pi)/(2)-sin^(-1)(sin.(theta)/(2)))` `=cos theta-pi+theta` `therefore" "y=x-pi+cos^(-1)x` `therefore" "(dy)/(dx)=1-(1)/(sqrt(1-x^(2)))`

The derivative of `cos(2tan^(-1)sqrt((1-x)/(1+x)))-2cos^(-1)sqrt((1-x)/(2))` w.r.t. x isA. `1-(1)/(sqrt(1-x^(2)))`B. `1-(1)/(sqrt(1+x^(2)))`C. `2-(1)/(sqrt(1-x^(2)))`D. `2-(1)/(sqrt(1+x^(2)))`
`(d)/(dx)[cos^(-1)(xsqrtx-sqrt((1-x)(1-x^(2))))]=`A. `(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))`B. `(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))`C. `(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))`D. `(1)/(sqrt(1-x^(2)))`
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