In a right angle triangle, we'll note one cathetus as b and the other one as c and the hypothenuse as a.

According to the rule of 30 degrees angle, a cathetus opposite to the angle pi/6 (meaning 30 degrees) is half from hypothenuse.

If b is the opposite cathetus to pi/6 angle, that means that b=a/2.

In this way, we can find the other cathetus length, using Pythagorean theorem.

a^2=b^2 + c^2

a^2 = a^2/4 + c^2

a^2 - a^2/4 = c^2

3a^2/4 = c^2

[a*sqrt(3)]/2=c

cos pi/6=adjacent cathetus/hypotenuse

cos pi/6= [a*sqrt(3)]/2/a

cos pi/6=sqrt3/2

sin pi/3=sin 60=opposite cathetus/hypotenuse

sin pi/3= [a*sqrt(3)]/2/a

sin pi/3 = sqrt3/2

cos pi/6+sin pi/3 = sqrt3/2 + sqrt3/2

cos pi/6+sin pi/3 = 2sqrt3/2

**cos pi/6+sin pi/3 = sqrt 3**

To find cospi/6+sinpi/3.

We know that cos pi/ = sinpi3 = (sqrt/3)/2

Therefore , cospi/6 + sin pi/3 = 2(sqrt3)/2 = sqrt3.