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cos pi/6 + + sinpi/3
We know that:
cos pi/6 = cos 30 = sqrt3/2
sin pi/3 = sin60 = sqrt3/2
cos pi/6 + sin pi/3 = sqrt3/2 + sqrt3/2
= 2sqrt3/2 = sqrt3
==> cos pi/6 + sin pi/3 = sqrt3
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
cos pi/6=adjacent cathetus/hypotenuse
cos pi/6= [a*sqrt(3)]/2/a
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.
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