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

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Let ABC be right angled triangle with angle B = 90 deg, angle A= pi/6 and angle C = cospi/6.

Angle A+B+C = pi/6+pi/2+p/3 =( p1+3pi+2pi)/6 = pi which is inaccordance with the sum of the 3 angles should be 180 degree.

Now Sin A - SinC = sinA = pi/6 - cosppi/3 .

But sinA = sinpi/6 = BC/AC.

Cos pi/3 = BC/AC.

Therefore sinpi/3 - cospi/3= 0

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