In a right angle triangle solve the expression : sinpi/6 - cospi/3 .

In a right angle triangle, where one cathetus is b and the
other one is c and the hypothenuse is a, 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(3)^1/2]/2=c

sin
pi/6=opposite cathetus/hypotenuse

sin pi/6=
(a/2)/a

sin pi/6=1/2

cos
pi/3=cos 60=adjacent cathetus/hypotenuse

cos pi/3=
(a/2)/a

cos pi/3=1/2

sin pi/6
- cos pi/3=1/2 -1/2=0