Question

If $-1+\cos {56}^{\circ }+\cos {58}^{\circ }+\cos {66}^{\circ }=k\sin {28}^{\circ }\sin {29}^{\circ }\sin {33}^{\circ }$ , then the value of k is

• A. $1$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (C)

$4$

$-1+\cos 56+\cos 58+\cos 66$

$=-1+\cos 56+\cos 58+\cos (180-114)$

$=-1+2\cos 57\cos 1-2{\cos }^{2}57+1$

$=2\cos 57(\cos 1-\cos 57)$

$=2\cos (90-33)\left(2\sin 29\sin 28\right)$

$=4\sin 28\sin 29\sin 33$