Question

differentiate tan x - cos x / sinx.cosx

Answer 1

Hey...✌
Solution:

$\frac{ \tan(x) - \cos(x) }{ \sin(x) .\cos(x) } \\ \\ = \frac{ \tan(x) }{ \sin(x) .\cos(x) } - \frac{ \cos(x) }{ \sin(x) .\cos(x) } \\ \\ = \frac{1}{ \cos ^{2} (x) } - \frac{1}{ \sin(x) } \\ \\ = sec ^{2}(x) - cosec(x) \\ \\ differentitaing \: wrt \: x \:we \: get \\ \\ = > 2sec ^{2} (x) \tan(x) + cosec(x)cot(x)$