3sinx=2.5-cosx.
Square both sides:
9sin^2x=6.25+cos^2x-5cosx.
9(1-cos^2x)=6.25+cos^2x-5cosx.
9-9cos^2x=6.25+cos^2x-5cosx.
10cos^2x-5cosx-2.75=0.
cos^2x-0.5cosx-0.275=0.
Completing the square:
(cos^2x-0.5cosx+0.0625)-0.0625-0.275=0.
(cosx-0.25)^2=0.3375.
Square root of each side:
cosx-0.25=+0.58095 approx, so cosx=0.25+0.58095, cosx=0.83095 or -0.33095.
x=-33.80°, 33.80°, 109.33°, -109.33°.
Of these tentative solutions, 33.80° and 109.33 are valid.
But, we need to check in the original equation:
3sinx+cosx=