SOLUTION: 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.

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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.
LET A = 22.5...LET SIN(A)=X TO BE FOUND OUT..
2A=2*22.5=45
COS(2A)=1-2*{SIN(A)}^2
COS(45)=1-2X^2
1/SQRT(2)=1-2X^2
2X^2=1-1/SQRT(2)=1-SQRT(2)/2=(2-SQRT(2))/2
X^2=(2-SQRT(2))/4
X=SQRT{2-SQRT(2)}/2
=0.3827