5 Sin A+ 3COS A= 4 ----> eq 1 3 Sin A- 5 Cos A = x -----> eq 2 squaring and adding both the equations: (5 sin A+3 cos A)²+ (3SIN A-5Cos A)² = 4²+x² 25 sin²A+ 2×3×5 SinA cos A+ 9cos²A + 9²sinA - 2×3×5 sinA cos A + 25 Cos²A = 4² + x² rearranging : 25 sin ²A + 25Cos²A+9 sin²A +9cos²A+30 sinAcosA-30SinAcosA= 16+x² (since sin²A+cos²A = 1) 25+9 = 16+x² x² = 34 x =4.242