Question

acosx+bsinx+c/sinx+ x^n cosx​

Answer 1

a cos x+b sin x= c , divide both sides by(a^2+b^2)^1/2.

a/(a^2+b^2)^1/2.cos x+b/(a^2+b^2)^1/2.sin x=c/(a^2+b^2)^1/2.

Let a/(a^2+b^2)^1/2=sin A , then b/(a^2+b^2)^1/2=cosA

sinA.cos x+cos A.sin x=c/(a^2+b^2)^1/2

sin (A+x)= c/(a^2+b^2)^1/2

A+x=sin inverse c/(a^2+b^2)^1/2

x=sin inverse c/(a^2+b^2)^1/2-A

x=sin inverse c/(a^2+b^2)^1/2 - sin inverse a/(a^2+b^2)^1/2. , answer.