Can someone check this method

[orchid trout]

I know that the answer is correct but I would like to know whether this method is valid. We can equate the coefficents because it is said that A,B is constant?

[sharp granite]

if I am not misunderstanding you, the answer to your question should be a yes.

[verbal flame]

yes we absolutely can

[gray forge]

Well done,

[pure spire]

there is a general formula for this https://www.desmos.com/calculator/93neomiap5

but for acosx + bsinx its r(sinx+phi) where r=sqrt(a^2+b^2) and phi=tan^-1(a/b)