InterviewSolution
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InterviewSolution
| 1. |
Prove that \cos 16^{\circ} \cos 42^{\circ} \cos 66^{\circ} \cos 78=\frac{1}{16} |
| Answer» <p>LHS= (cos 6) (cos 42)(cos 66) (cos 78)= (1/4) * [2cos6 cos66] * [2cos42 cos78]= (1/4) * (cos72 + cos60) * (cos120 + cos36)= (1/4) (cos72 + 1/2) * (- 1/2 + cos36)= (1/4) [- 1/4 + (1/2) (cos36 - cos72) + cos36cos72]= (1/4) [- 1/4 + sin54sin18 + sin54 sin18]= (1/4) [- 1/4 + 2sin54 sin18 cos18 / cos18]= (1/4) [- 1/4 + 2sin54 sin36 / cos18]= (1/4) [- 1/4 + (cos18 - cos90) / 2cos18]= (1/4) [- 1/4 + 1/2]= 1/16= RHS</p> | |