How do you use a half-angle formula to find the exact value of #cos22.5#?
2 Answers
Aug 10, 2018
Explanation:
Let
cos (theta/2) = cos 22.5^@ = + sqrt((1 - cos 45) / 2)#
We know
Aug 10, 2018
Explanation:
#"using the "color(blue)"half-angle formula for cos"#
#•color(white)(x)cos(x/2)=+-sqrt((1+cosx)/2)#
#cos22.5^@=+sqrt((1+cos45^@)/2)#
#color(white)(xxxxxx)=sqrt((1+sqrt2/2)/2)#
#color(white)(xxxxxx)=sqrt((2+sqrt2)/4)#
#color(white)(xxxxxx)=1/2(sqrt(2+sqrt2))#