find the exact value of the expression.

Question

2cos^2 x 67.5 degrees -1

a)-1/2

b)sqrt2/2

c)-sqrt3

d)1/2

e)sqrt3

f)-sqrt2/2

Answer 1

2cos^2(67.5°)-1

cos2θ=2cos^2θ-1 is a trig identity

change this identity around to get...

cos2θ+1=2cos^2θ

substitute

cos(2*67.5°)+1-1

cos(135°)

now look on the unit circle and find cos135°

cos135°=-√2/2 which is f.