Question

Ifcos x + cos y + cos a=0 and sin x + sin y + sin a=0 x+y then cot (x+y/ 2) =​

Answer 1

Answer:

cot a

Step-by-step explanation:

cos x + cos y + cos α = 0

cos x + cos y = -cos α

2 cos(x + y)/2 cos(x – y)/2 = -cos α….(i)

sin x + sin y + sin α = 0

sin x + sin y = -sin α

2 sin(x + y)/2 cos(x – y)/2 = -sin α….(ii)

Dividing (i) by (ii),

[2 cos(x + y)/2 cos(x – y)/2]/ [2 sin(x + y)/2 cos(x – y)/2] = (-cos α)/(-sin α)

cot(x + y)/2 = cot α