Question

Evaluate , sin 105( degree ) + cos 105( degree )

Answer 1

sin(15) = sin(45-30) sin45*cos30 - cos45*sin30 =>(1/√2)*(√3/2) - (1/√2)*(1/2) =>√3/2√2 - 1/2√2 =>(√3 - 1) /2√2
similarly cos (15) = (√3 + 1) /2√2
sin (90-(-105)) + cos (90-(-105))
= -sin 15 +(-cos 15)
=-(√3 - 1) /2√2 + - (√3 + 1) /2√2
the ans is √3/ √2