# Solve the expression sin pi/6 - cos pi/3 .

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sin(pi/6) -cos(pi/3)

sin (pi/6)= sin(180/6)

= sin (30)=1/2

cos (pi/3)= cos(180/3)= cos(60)=1/2

Then sin(pi/6)-cos(pi/3)=1/2 - 1/2 =0

To solve sin pi/3 - cospi/6

Solution:

sin pi/3 = 1/2.

we know that cospi/6 = sin(pi/2-pi/6) = sinpi/3

Therefore sinpi/3 - cos pi/6 = sipi/3-sipi/3 = 0

First, we'll notice that we'll have to calculate the difference of 2 complementary functions of 2 complementary angles.

We know that sin pi/6 = cos (pi/2 - pi/6) = cos (2pi/6) = cos pi/3

We'll substitute in the given expression sin pi/6 by cos pi/3 and we'll get:

** cos pi/3 - cos pi/3 = 0**

**Note:** Also, we could substitute the functions by their values, knowing that

sin pi/6=1/2 and cos pi/3=1/2

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