(3 cos x-4 sin x)+(3sin x+4 cos x)=5 (3cos x+4cos x)+(-4sin x+3 sin x)=5 7 cos x-sin x=5 7cos x=5+sin x (7 cos x)²=(5+sinx)² 49 cos²x=25+10 sinx+sin²x 49(1-sin²x)=25+10 sinx+sin²x 49-49sin²x=25+10sinx+sin²x 50 sin² x+10sinx-24=0
Sin x=[-10⁺₋√(100+4800)]/100=(-10⁺₋70)/100 We have two possible solutions: sinx =(-10-70)/100=-0.8 x=sin⁻¹ (-0.8)=-53.13º (360º-53.13º=306.87)
sinx=(-10+70)/100=0.6 x=sin⁻¹ 0.6=36.87º
The solutions when 0≤x≤360º are: 36.87º and 306.87º.
