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

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

cdquestions Admin · Accepted Answer

$\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}$ $⇒2 \sin\dfrac{3π}{14} \cos \dfrac{3π}{14} = 2k \cos \dfrac{π}{14}$   $⇒\sin\dfrac{6π}{14} =2k \cos \dfrac{π}{14}$   $\therefore( \dfrac{6π}{14} +\dfrac{π}{14} = \dfrac{7π}{14} = \dfrac{π}{2} )$ $\sin \dfrac{6π}{14} = \cos\dfrac{ π}{14}$ 1 = 2k $\therefore 4k=4×\dfrac{1}{2}$ $\therefore k=2$ So, the correct option is (B) : 2.

Answer

$1$

Answer

$2$

Answer

$3$

Answer

$4$

Answer

$0$

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

The Correct Option is B

Solution and Explanation

Top Questions on Trigonometry

Questions Asked in KEAM exam