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

Question

cdquestions Admin · Accepted Answer

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

Answer

(A)

\frac{3}{5}

Answer

(B)

\frac{3}{5}

Answer

(C)

\frac{3}{5}

Answer

(D)

\frac{3}{5}

If $\sin (α + β) = 6 \sin (α - β)$ and $k = \frac{\tan α}{\tan β}$ , then, what is the value of $k$ ?

The Correct Option is D

Solution and Explanation

Top Questions on Continuity and differentiability

Questions Asked in MHT CET exam

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

The Correct Option is D

Solution and Explanation

Top Questions on Continuity and differentiability

Questions Asked in MHT CET exam

If $\sin (α + β) = 6 \sin (α - β)$ and $k = \frac{\tan α}{\tan β}$ , then, what is the value of $k$ ?