If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)

• Quant Trigo

If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)?

1. 0
2. 2
3. 3
4. 5

Solution

(3 sin x + 5 cos x)² = 5²

9 sin² x + 25 cos² x + 30 sin x cos x = 25 [Equation 1]

(3 cos x – 5 sin x)² = k²

9 cos² x + 25 sin² x - 30 sin x cos x = k² [Equation 2]

Add both equations: 9 + 25 = 25 + k²

k = 3

The correct option is C.