Question

Cos85° *cos40°-sin85°*sin(-40°)
--------------------------------- =
Sin40°*cos5°+cos40°*sin5°

Answer 1

$\frac{cos85cos40+sin85sin40}{sin40cos5+cos40sin5}= \frac{cos(85-40)}{sin(40+5)}= \frac{cos45}{sin45}=ctg45=1$

Answer 2

cos85⁰*cos40⁰ - sin85⁰*sin(-40⁰) = cos85⁰*cos40⁰ + sin85⁰*sin40 = cos(85-40) = cos 45⁰ = $\frac{ \sqrt{2} }{2}$

sin40⁰*cos5⁰+cos40⁰sin5⁰ = sin (40+5) = sin 45⁰ = $\frac{ \sqrt{2} }{2}$

$\frac{ \sqrt{2} }{2} : \frac{ \sqrt{2} }{2} = 1$