If 3 sin Theta 5 cos Theta 5 then the value of 5 sin Theta ndash 3 cos Theta will be ........

Quantitative Aptitude ( CCS) Trignometry

Download Solution PDF

If 3 sin Θ + 5 cos Θ = 5, then the value of 5 sin Θ – 3 cos Θ will be

± 3

± 5

± 2

± 1

छोटे Courses बड़े Results

Master Trignometry

Prepare through Micro-courses

Try Now

Explanation:

From the given equation,
3 sin Θ + 5 cos Θ = 5
∴ (3 sin Θ + 5 cos Θ)² = 5²
∴ 9 sin² Θ + 25 cos² Θ + 30 sin Θ cos Θ = 25
∴ 9(1 – cos² Θ) + 25(1 – sin² Θ) + 30 sin Θ cos Θ = 25
∴ 9 – 9cos² Θ + 25 – 25sin² Θ + 30 sin Θ cos Θ = 25
∴ 9 = 25 sin² Θ + 9 cos²Θ – 30 sin Θ cos Θ
∴ 9 = (5 sin Θ – 3 cos Θ)²
∴ 5 sin Θ – 3 cos Θ = ±√9
∴ 5 sin Θ – 3 cos Θ = ± 3.