Question

y =loge tan(x/2) then y' = ?
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Answer 1

Explanation:

1. given y=log tan(x/2)
2. let tan(x/2) =z
3. y'=(1/z) ×z'
4. y'=(1/tan(x/2))×sec^2(x/2)×1/2
5. y'=(1/tan(x/2))×sec^2(x/2)×1/2
6. sec^2(x/2)/tan(x/2)=1/(2×sin(x/2)×cos(×/2)
7. =1/sin(x)=cosec(x)
8. y'=cosec(x)