Prove that cosa*cosb

We'll consider the constraint a - b = pi => a = pi
+ b

We'll calculate the cosine function of the angle
a:

cos a = cos (pi + b)

We'll
use the following identity:

cos (x+y) = cosx*cosy -
sinx*siny

Comparing, we'll
get:

cos (pi + b) = cos pi*cos b - sin pi*sin
b

But cos pi = - 1 and sin pi =
0

cos (pi + b) = -cos
b

Therefore cos a = - cos
b.

If we'll multiply a negative number by a
positive number, the result is a negative number, therefore cos a*cos b = - (cos b)^2
=<0.