How do you find the exact value of cos pi/6 cos pi/3 - sin pi/6 sin pi/3? Trigonometry Right Triangles Trigonometric Functions of Any Angle 1 Answer Ratnaker Mehta Aug 10, 2018 # 0.# Explanation: Recall that, #cosxcosy-sinxsiny=cos(x+y)#. Hence, with #x=pi/6 and y=pi/3#, we have, #cos(pi/6)cos(pi/3)-sin(pi6)sin(pi/3)#, #=cos(pi/6+pi/3)#, #=cos(pi/6+2pi/6)#, #=cos(3pi/6)#, #=cos(pi/2)#, #=0#. Answer link Related questions How do you find the trigonometric functions of any angle? What is the reference angle? How do you use the ordered pairs on a unit circle to evaluate a trigonometric function of any angle? What is the reference angle for #140^\circ#? How do you find the value of #cot 300^@#? What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#? How do you know if #sin 30 = sin 150#? How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle Impact of this question 6425 views around the world You can reuse this answer Creative Commons License