sin(pi/3 - a) = sin(pi/3)cos(a) - cos(pi/3)sin(a)= sqrt(3)/2 cos(a) - 1/2 sin(a)
cos(pi/4 + a) = cos(pi/4)cos(a) - sin(pi/4)sin(a)= 1/sqrt(2) cos(a) - 1/sqrt(2) sin(a)
tg(pi/4 - a) = [tan(pi/4) - tan(a)] / [1 + tan(pi/4)tan(a)]= [1 - tan(a)] / [1 + tan(a)]
sin(2a) = 2sin(a)cos(a)
cos(2a) = cos^2(a) - sin^2(a)
tan(2a) = sin(2a) / cos(2a)= 2/3 cosec(a) * cot(a)
sin(pi/3 - a) = sin(pi/3)cos(a) - cos(pi/3)sin(a)
= sqrt(3)/2 cos(a) - 1/2 sin(a)
cos(pi/4 + a) = cos(pi/4)cos(a) - sin(pi/4)sin(a)
= 1/sqrt(2) cos(a) - 1/sqrt(2) sin(a)
tg(pi/4 - a) = [tan(pi/4) - tan(a)] / [1 + tan(pi/4)tan(a)]
= [1 - tan(a)] / [1 + tan(a)]
sin(2a) = 2sin(a)cos(a)
= 2 * (1/3) * cos(a)cos(2a) = cos^2(a) - sin^2(a)
= cos^2(a) - (1/9)tan(2a) = sin(2a) / cos(2a)
= 2/3 cosec(a) * cot(a)