`cos^(- 1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2)))`

1.	`cos^(- 1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2)))`
Answer» `cos^(-1)sqrt(((1+x^2)+1)/(2sqrt(1+x^2))` Let `x=tantheta` `1+x^2=1+tan^2theta=secc^2theta` `=cos^(-1)sqrt((sqrt(sec^2theta)+1)/(2sqrtsec^2theta))` `=cos^(-1)sqrt((sectheta+1)/(2sectheta))` `=cos^(-1)sqrt((1+costheta)/2)` `cos2theta=2cos^2theta-1` `1+cos2theta=2cos^2theta` `1+costheta=2cos^2(theta/2)` `cos^(-1)sqrt(1/2(2cos^2(theta/2)))` `cos^(-1)sqrt(cos^2(theta/2))` `cos^(-1)(cos(theta/2))` `theta/2` `1/2tan^(-1)x`.

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`cos^(- 1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x^2)))`

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