Question

What is the value of Sin(22•1/2)°

Answer 1

cos45=cos^2(45/2)-sin^2(45/2)
1/√2=1-2sin^2(45/2)
2sin^2(45/2)=1-(1/√2)
sin(45/2)=√[√2-1/2√2]

Answer 2

We know, formula
$cos2{\theta} = 1-2sin^2{\theta}\\\\sin(45) =1-2sin^2(\frac{45}{2})\\\\\frac{1}{\sqrt{2}}=1-2sin^2(\frac{45}{2})\\\\\frac{(1-\sqrt{2})}{\sqrt{2}}=-2sin^2(\frac{45}{2})\\\\\frac{(\sqrt{2}-1)}{2\sqrt{2}}=sin^2(\frac{45}{2}\\\\sin(\frac{45}{2})=\sqrt{\frac{(\sqrt{2}-1)}{2\sqrt{2}}$