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Assume that 0 < x < pi/2 and 0 < y < pi/2.  Find the exact value of cos(x - y) if cos(x) = 3/5 and cos(y) = 4/5.

 

 Apr 21, 2020
 #1
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draw a triangle to find sin(x) and sin(y)

(little drawing thing)

 

sin(x) = 4/5, sin(y) = 3/5 from the picture

 

cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
= (3/5)(4/5) + (4/5)(3/5) = 12/25 + 12/25 = 24/25

 Apr 21, 2020

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