Question

If 3sinθ+5cosθ = 5, prove that 5sinθ-3cosθ = ±3​

Answer 1

Step-by-step explanation:

GIVEN

• 3 sinθ + 5 cosθ = 5

SOLUTION

Squaring both sides, we get

• (3 sinθ + 5 cosθ)² = 5²
• 9 sin²θ + 30 sinθ cosθ + 25 cos²θ = 25
• 9 (1 - cos²θ) + 30 sinθ cosθ + 25 (1 - sin²θ) = 25
• 9 - 9 cos²θ + 30 sinθ cosθ + 25 - 25 sin²θ = 25
• 25 sin²θ - 30 sinθ cosθ + 9 cos²θ = 9
• (5 sinθ - 3 cosθ)² = 3²
• 5 sinθ - 3 cosθ = ±3

Answer 2

Step-by-step explanation:

square both side

take common factor

convert it to Algerabic identity