Question

If 3sinθ + 5cosθ=5, then find the value of 5sinθ-3cosθ.

Answer 1

$\textbf{Answer :}$

Given,

3 sinθ + 5 cosθ = 5

Now, 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,

which is the required answer.

#$\textbf{MarkAsBrainliest}$