

InterviewSolution
Saved Bookmarks
1. |
Prove that `4cos12^@cos48^@cos72^@=cos36^@` |
Answer» Here, we will use the following rules, `2cosAcosB = cos(A+B)+cos(A-B)` `cosA+cos B = 2cos((A+B)/2)cos((A-B)/2)` `L.H.S. = 4cos12^@cos48^@cos72^@` `=2cos72^@(cos(48+12)^@+cos(48-12)^@)` `=2cos72^@(cos60^@+cos36^@)` `=2cos72^@(1/2+cos36^@)` `=cos72^@ +2cos72^@cos36^@` `=cos72^@ +cos(72+36)^@+cos(72-36)^@` `=cos72^@+cos108^@+cos36^@` `=2cos((108+72)/2)^@cos((108-72)/2)^@+cos36^@` `=2cos90^@cos36^@+cos36^@` `=0+cos36^@ = cos36^@=R.H.S.` |
|