What is the value of cos[pi/3-pi/4]?

1 Answer
Nghi N.
Jul 29, 2016

(sqrt2 + sqrt6)/4

Explanation:

Apply the trig identity:
cos (a - b) = cos a.cos b + sin a.sin b
cos (pi/3 - pi/4) = cos (pi/3).cos (pi/4) + sin (pi/3).sin (pi/4) =
Trig table of special arcs gives:
cos (pi/3) = 1/2 , and cos (pi/4) = sqrt2/2
sin (pi/3) = sqrt3/2, and sin (pi/4) = sqrt2/2
There for:
cos (pi/3 - pi/4) = (1/2)(sqrt2/2) + (sqrt3/2)(sqrt2/2) =
= sqrt2/4 + sqrt6/4 = (sqrt2 + sqrt6)/4

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