Question

Let $k$ be a real number such that $\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}$.Then the value of $4k$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$
• E. $0$

Answer 1

Answer: (B)

$2$

Answer 2

$\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}$

$⇒2 \sin\dfrac{3π}{14} \cos \dfrac{3π}{14} = 2k \cos \dfrac{π}{14}$

$⇒\sin\dfrac{6π}{14} =2k \cos \dfrac{π}{14}$

$\therefore( \dfrac{6π}{14} +\dfrac{π}{14} = \dfrac{7π}{14} = \dfrac{π}{2} )$

$\sin \dfrac{6π}{14} = \cos\dfrac{ π}{14}$
1 = 2k
$\therefore 4k=4×\dfrac{1}{2}$
$\therefore k=2$
So, the correct option is (B) : 2.