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Question
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Solution
Let y = `log[tan(x/2)]`
Differentiating w.r.t. x, we get,
`"dy"/"dx" = "d"/"dx"log[tan(x/2)]`
= `1/tan(x/2)."d"/"dx"[tan(x/2)]`
= `1/tan(x/2).sec^2(x/2)."d"/"dx"(x/2)`
= `cos(x/2)/(sin(x/2)).(1)/cos^2(x/2).(1)/(2) xx 1`
= `1/(2sin(x/2)cos(x/2)`
= `(1)/sinx`
= cosec x.
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