Question

If sin⁡(α+β)=6sin⁡(α−β) and k=tan⁡αtan⁡β, then, what is the value of k ?

• A. (A) 35
• B. (B) 65
• C. (C) 45
• D. (D) 75

Answer 1

Answer: (D)

(D) 75

Answer 2

Explanation:
Given,sin⁡(α+β)=6sin⁡(α−β) and k=tan⁡αtan⁡βsin⁡(α+β)=6sin⁡(α−β)⇒sin⁡αcos⁡β+cos⁡αsin⁡β=6sin⁡αcos⁡β−6cos⁡αsin⁡β⇒cos⁡αsin⁡β+6cos⁡αsin⁡β=6sin⁡αcos⁡β−sin⁡αcos⁡β⇒7cos⁡αsin⁡β=5sin⁡αcos⁡β⇒sin⁡αcos⁡α=75×sin⁡βcos⁡β⇒ tan α=75×tan⁡β⇒k=tan⁡αtan⁡β=75∴ The value of k is 75
Hence, the correct option is (D).