How do you find the exact value of cos pi/6 cos pi/3 - sin pi/6 sin pi/3?

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Answer 1 · 2018-08-10T06:32:10

# 0.#

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#.