How to find the exact value of sin 22.5° and tan 7.5° using double angle formula?

Answer 1

We use that 2(22,5)=45 and the formula (sinx)^2=(1-cos2x)/2. Then we obtain

(sin22,5)^2=(1-cos45)/2=(2-sqrt(2))/4 and since sin(22,5)>0 we get that sin(22,5)=sqrt((2-sqrt(2))/4).

For tan(7,5) you have to apply two times the double angle formula to go from 7,5 to 15 and then to 30 since we know explicitly the values of sin and cos for 30 degrees.