Question

How do you use half angle formula to find sin 75?

Answer 1

`sqrt(1+sqrt3/2)`

Half angle formula for sine is `sin (x/2)= sqrt[(1-cosx)/2]`. If x is 150, then sin 75= `sqrt((1-cos150)/2)`
=`sqrt((1-cos(180-30)/2)`
= `sqrt((1+cos30)/2)`
= `sqrt(1/2+sqrt3/4)`

This can also be expressed as `(sqrt6 +sqrt2)/4`