Evaluate : 16cos (2π/15) cos (4π/15) cos (8π/15) cos (16π/15)

Asked by tps.mjmdr | 16th Jun, 2018, 05:50: PM

Expert Answer:

begin mathsize 16px style 16 cos open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 16 straight pi over denominator 15 end fraction close parentheses
equals 16 cos open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses cos open parentheses straight pi plus straight pi over 15 close parentheses
equals negative 16 cos open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses cos open parentheses straight pi over 15 close parentheses
equals fraction numerator negative 8 over denominator sin straight pi over 15 end fraction cross times 2 sin straight pi over 15 cos open parentheses straight pi over 15 close parentheses cos open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses
equals fraction numerator negative 8 over denominator sin straight pi over 15 end fraction cross times sin open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses
equals fraction numerator negative 4 over denominator sin straight pi over 15 end fraction cross times 2 sin open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 2 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses
equals fraction numerator negative 2 over denominator sin straight pi over 15 end fraction cross times 2 sin open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses
equals fraction numerator negative 2 over denominator sin straight pi over 15 end fraction cross times sin open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 4 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses
equals fraction numerator negative 1 over denominator sin straight pi over 15 end fraction cross times 2 sin open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses cos open parentheses fraction numerator 8 straight pi over denominator 15 end fraction close parentheses
equals fraction numerator negative 1 over denominator sin straight pi over 15 end fraction cross times sin open parentheses fraction numerator 16 straight pi over denominator 15 end fraction close parentheses
equals fraction numerator negative sin open parentheses straight pi plus begin display style straight pi over 15 end style close parentheses over denominator sin straight pi over 15 end fraction
equals fraction numerator sin straight pi over 15 over denominator sin straight pi over 15 end fraction equals 1 end style

Answered by Sneha shidid | 18th Jun, 2018, 10:46: AM