Question

Sin 15 degree and 15 degree is rational number

Answer 1

sin15°=sin(45°-30°)
Now using sin(A-B) formula
sin(45-30)=sin45°cos30°-cos45°sin30°
=(1/√2) x(√3/2)-(1/√2) x(1/2)
=(√3/2√2)-(1/2√2)
=(√3-1)/2√2
multiplying numerator and denominator by √2 we get
=(√6-√2)/4
which is an irrational number(since irrational/rational=irrational no.)
also 180°=π rad
1°=π/180 rad
15°=π/12 rad which is an irrational number(since irrational/rational=irrational no.)