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As per trigonometric identities, cot x can also be written as cosxsinx
Now we can use quotient rule of differentiation to find the derivative of cotx.
Quotient rule: d(uv)dx=(vdudx−udvdx)v2
Here u=cosx, v=sinx
We can substitute the formulae for the derivatives of sin x and cos x given by
d(cosx)dx=−sinx and d(sinx)dx=cosx
On putting the above values in equation (ii), we get
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