1.

`cos""(2pi)/(15)cos""(4pi)/(15)cos""(8pi)/(15)cos""(16pi)/(15)=(1)/(16)`

Answer» True
`" "LHS=cos""(2pi)/(15)cos""(4pi)/(15)cos""(8pi)/(15)cos""(16pi)/(15)`
`" "=cos24^(@)cos48^(@)cos96^(@)cos192^(@)`
`" "=(1)/(16sin24^(@))[(2sin24^(@)cos24^(@))(2cos48^(@))(2cos96^(@))(2cos192^(@))]` ltBrgt `" "=(1)/(16sin24^(@))[2sin48^(@)cos48^(@)(2cos96^(@))(2cos192^(@))]`
`" "=(1)/(16sin24^(@))` `[(2sin96^(@)cos96^(@))(2cos192^(@))]`
` " "=(1)/(16sin24^(@))[2sin192^(@)cos192^(@)]`
`" "=(1)/(16sin24^(@))sin384^(@)=(sin(360^(@)+24^(@)))/(16sin24^(@))`
`" "=(1)/(16)=RHS" "` Hence proved


Discussion

No Comment Found

Related InterviewSolutions