Maharashtra State BoardHSC Science (General) 11th
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Prove the following: cos(x + y).cos(x − y) = cos2y − sin2x - Mathematics and Statistics

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Sum

Prove the following:

cos(x + y).cos(x − y) = cos2y − sin2x

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Solution

L.H.S. = cos(x + y) · cos (x – y)

= (cosx cosy – sinx siny) · (cosx cosy + sinx siny)

= cos2x cos2y – sin2x sin2y .....[∵ (a − b) (a + b) = a2 − b2]

= (1 – sin2x) cos2y – sin2x (1 – cos2y) ......[∵ sin2θ + cos2θ = 1]

= cos2y – sin2x cos2y – sin2x + sin2x cos2y

= cos2y – sin2x

= R.H.S.

Concept: Trigonometric Functions of Multiple Angles
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