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Question
Prove the following:
`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`
Solution
L.H.S. = `(cos(x - y))/(cos(x + y))`
= `(cosx cosy + sinx siny)/(cos x cos y - sin x sin y)`
Dividing numerator and denominator by sin x sin y, we get
L.H.S. = `(((cosx cosy)/(sinx sin y) + 1))/(((cosx cos y)/(sinx sin y) - 1)`
= `(cotx coty + 1)/(cotx coty - 1)`
= R.H.S.
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