given:

is a solution of the given equation

To find: solution of given differential equation

Re-writing the given equation as

It is a first order linear differential equation

Comparing it with

p(x)=cot x

q(x)=2 cos x

Calculating integrating factor

Formula:

IF = sin x

Therefore, the solution of the differential equation is given by

Substituting to get the value of c

Therefore, the solution is