Its asking truefalse needing to determine without a calculat

It\'s asking true/false, needing to determine without a calculator. Please explain it! Thank you!

Solution

sin (180+20)= - sin 20

so

sin 20 = sqrt((1-cos40)/2)

as we know sin²(x) = (1-cos(2x))/2

so,

sin 20= sqrt(sin^2 20)

so

sin 20= sin 20

lhs=rhs

hence proved