Maharashtra State BoardHSC Science (Electronics) 11th
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Prove the following: cos(x-y)cos(x+y)=cotxcoty+1cotxcoty-1 - Mathematics and Statistics

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Sum

Prove the following:

`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`

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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.

Concept: Trigonometric Functions of Sum and Difference of Angles
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