How do you express cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 ) cos(15π8)cos(15π8) without using products of trigonometric functions?

1 Answer
Mar 13, 2016

1/2+1/2cos(pi/4)12+12cos(π4)

Explanation:

cos((15pi)/8)*cos((15pi)/8)=cos^2((15pi)/8)cos(15π8)cos(15π8)=cos2(15π8)

As cos2A=2cos^2A-1cos2A=2cos2A1, cos^2A=1/2+(cos2A)/2cos2A=12+cos2A2

Hence cos((15pi)/8)*cos((15pi)/8)=1/2+1/2cos((15pi)/4)cos(15π8)cos(15π8)=12+12cos(15π4)

= 1/2+1/2cos(4pi-pi/4)12+12cos(4ππ4)

= 1/2+1/2cos(-pi/4)=1/2+1/2cos(pi/4)12+12cos(π4)=12+12cos(π4)