How do you find the exact value cos(x-y) if cosx=3/5,cosy=4/5

musicintimeln

musicintimeln

Answered question

2022-08-11

How do you find the exact value cos ( x y ) if cos x = 3 5 , cos y = 4 5 ?

Answer & Explanation

Brogan Navarro

Brogan Navarro

Beginner2022-08-12Added 24 answers

Use trig identity:
cos ( x y ) = cos x cos y + sin x sin y
We have cos x = 3 / 5, find sin x
We have cos y = 4 / 5, find sin y
sin x = 1 cos 2 x = 1 9 25 = 16 25 sin x = ± 4 5
sin y = 1 cos 2 y = 1 16 25 = 9 25 sin y = ± 3 5
Since cos x > 0 and cos y > 0, then the arcs x and y are both located in Quadrant I. Their sin are both positive. There for:
cos ( x y ) = ( 3 5 ) ( 4 5 ) + ( 4 5 ) ( 3 5 ) = 24 25

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