Differentiate `cos^(-1){sqrt((1+cosx)/(2))}` w.r.t. x.

1.	Differentiate `cos^(-1){sqrt((1+cosx)/(2))}` w.r.t. x.
Answer» Let `y=cos^(-1){sqrt((1+cosx)/(2))}=cos^(-1){sqrt((2cos^(2)(x//2))/(2))}` `=cos^(-1){cos(x//2)}=(x)/(2).` `thereforey=(x)/(2).` Hence, `(dy)/(dx)=(d)/(dx)((x)/(2))=(1)/(2).`

Discussion

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