If 3 cot θ = 4 then \frac{\left(\right. 5 sinθ + 3 cosθ \left.\right)}{\left(\right. 5 sinθ

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If 3 cot θ = 4 then $\frac{(5 sinθ + 3 cosθ)}{(5 sinθ - 3 cosθ)} = ?$

$\frac{1}{3}$

$\frac{1}{9}$

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Given 3 cot θ = 4, so cot θ = 4/3. Therefore, cos θ/sin θ = 4/3. Let sin θ = 3k and cos θ = 4k for some constant k.

Substitute into the expression: $\frac{(5 (3 k) + 3 (4 k))}{(5 (3 k) - 3 (4 k))} = \frac{15 k + 12 k}{15 k - 12 k} = \frac{27 k}{3 k} = 9$

Final Answer: 9