Question

what is the exact value of sin 22.5 degrees using the sum, difference, half, or double angle formulas and the exact value chart in the solution.

Answer 1

$cos 2x=1-2sin^2x \\ cos 45^0=1-2sin^2(22,5)^0 \\ \frac{ \sqrt{2} }{2} =1-2sin^2(22,5)^0 \to sin(22,5)^0= \frac{ \sqrt{2- \sqrt{2} } }{2}$