How do you use a half-angle formula to simplify $cos [ - (3pi) / 8]$ ?

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Answer 1 · 2015-05-23T13:46:34

Use the trig identity: $1 + cos 2x = 2cos^2x$

$2cos^2((-3pi)/8) = 1 - cos ((-3pi)/4)$

Or $cos ((-3pi)/4) = cos ((3pi)/4) = -cos (pi/4)$ , then

$2cos^2 (-(3pi)/8) = 1 + cos (pi/4)= 1 + (sqrt2)/2$

$cos^2((-3pi)/8) = (2 + sqrt2)/4$

How do you use a half-angle formula to simplify cos [ - (3pi) / 8]cos [ - (3pi) / 8]?