How do you find the value of cos((7pi)/8) using the double or half angle formula?

1 Answer
Jan 6, 2017

cos ((7pi)/8)= -sqrt ((sqrt2 +1)/(2sqrt2))

Explanation:

Write cos(7pi)/8 = cos (pi-pi/8)= -cos pi/8

Now using half angle formula, cosx= 2 cos^2 (x/2) -1, we can write cos pi/4 = 2 cos^2 (pi/8) -1

This means 1/sqrt2 +1 = 2 cos^2 (pi/8)

2cos^2 (pi/8) = (sqrt2 +1)/sqrt2

cos^2 (pi/8) = (sqrt2 +1)/(2sqrt2)

cos (pi/8)= sqrt ((sqrt2 +1)/(2sqrt2))

Hence cos ((7pi)/8)= - cos (pi/8) = -sqrt ((sqrt2 +1)/(2sqrt2))