Evaluate result of cos pi/6+sin pi/3?

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