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

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Answer 1 · 2017-01-06T03:39:46

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

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

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