Question

prove that : cos (A-π) + sin (A+π÷2)=0

Answer 1

cos(A-π) + sin(A+π/2),

cos[-(π-A)] + sin(π/2+A),

cos(π-A) + cosA,

-cosA + cosA,

0,

hence

L.H.S=R.H.S

Answer 2

cos
$cos(a - \pi) + sin(a + \pi \div 2 \\ \\ cos( - \pi - a) + sin(\pi \div 2 + a) \\ \\ cos(\pi - a) + sin(\pi \div 2 + a) \\ \\ - cosa + cosa \\ so \: ans \: is0 \:$