Find cos9pi8 using addition or subtraction formulaSolutionco

Find cos(9pi/8) using addition or subtraction formula.

Solution

cos(9pi/8) = cos(pi+pi/8) =

cos(A+B) = cosAcosB -sinAsinB

cos(pi +pi/8) = cospicospi/8 - sinpi*sinpi/8 = -cospi/8

Use the double angle formula to find -cos(pi/8)

-cos(pi/8): cos2x = 2cos^2x -1

cosx= sqrt( cos2x+1)

cos(pi/8) = sqrt(cospi/4 +1)

= sqrt( 1/sqrt2 +1) = sqrt{ (1+sqrt2)/sqrt2 }