Prove that cos (a-b) - cos (a+b) = 2sina sinb

Question

Mister

Mathematics

15 May, 20:22

Prove that cos (a-b) - cos (a+b) = 2sina sinb

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Skyla · Answer 1

We know:

cos (a - b) = cos (a) cos (b) + sin (a) sin (b)

cos (a + b) = cos (a) cos (b) - sin (a) sin (b)

cos (a - b) - cos (a + b) = 2sin (a) sin (b)

L = cos (a) cos (b) + sin (a) sin (b) - (cos (a) cos (b) - sin (a) sin (b))

= cos (a) cos (b) + sin (a) sin (b) - cos (a) cos (b) + sin (a) sin (b)

= 2sin (a) sin (b) = R