Question

if a = 30 then prove

Answer 1

sin^2 a + cos ^2 - 2 sina cos a
1 - √3/2 because 2sina cosa=sin2a prop.

sin 2a=√3/2
1-√3/2
so lhs = rhs

Answer 2

$(( \sin(a) - \cos(a) ) {}^{2} = 1 - \sin(2a) \\ sin {}^{2} a + \cos { }^{2}a - 2 \sin(a) \cos(a) = 1 - 2 \sin(a) \cos(a) \\ sin {}^{2} 30 + \cos^{2} 30 - 2 \sin(30) \cos(30) = 1 - 2 \sin(30) \cos(30) \\ (1 \div 2) {}^{2} + ( \sqrt{3} \div 2) {}^{2} - 2(1 \div 2)( \sqrt{3} \div 2) = 1 - 2(1 \div 2)( \sqrt{3} \div 2) \\ 1 \div 4 + 3 \div 4 - \sqrt{3} \div 2 = 1 - \sqrt{3} \div 2 \\ 1 - \sqrt{3} \div 2 = 1 - \sqrt{3} \div 2 \\ l.h.s = r.h.s \\ hence \: proved \\ thank \: you$