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Question
Differentiate the following w.r.t. x : `cos^-1(sqrt((1 + cosx)/2))`
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Solution
Let y = `cos^-1(sqrt((1 + cosx)/2))`
= `cos^-1(sqrt((2cos^2(x/2))/2))`
= `cos^-1[cos(x/2)]`
= `x/(2)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(x/2)`
= `(1)/(2)"d"/"dx"(x)`
= `(1)/(2) xx 1`
= `(1)/(2)`.
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