Step-by-step explanation:
proof from r.h.s to l.h.s
(cot(a)-tan(a))(cot(a)+tan(a))
cot(a)=cos(a)/sin(a)
tan(a)=sin(a)/cos(a)
(cot(a)-tan(a))=cos(a)/sin(a) - sin(a)/cos(a)
=cos²(a)-sin²(a)/sin(a)cos(a)
from trigonometry identity cos²(a)-sin²(a)=cos2(a)
so we have cos2(a)/sin(a)cos(a)
(cot(a)+tan(a))=cos(a)/sin(a) +sin(a)/cos(a)
=cos²(a)+sin²(a)/cos(a)sin(a)
from trigonometry identity cos²(a)+sin²(a)=so we have 1/cos(a)sin(a)
(cot(a)-tan(a)) ÷(cot(a)+tan(a))
=cos2(a)/cos(a)sin(a) ÷ 1/cos(a)sin(a)
=cos2(a)/cos(a)sin(a) * cos(a)sin(a)
=cos2(a)
proved
