Prove that :
$cos 2 α cos 2 β + sin^{2} (α - β) - sin^{2} (α + β) = cos 2 (α + β)$

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Prove that :

cos 2 α cos 2 β + sin^{2} (α - β) - sin^{2} (α + β) = cos 2 (α + β)

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Text solutionVerified

LHS :

cos 2 α cos 2 β + sin^{2} (α - β) - sin^{2} (α + β)

= cos 2 α cos 2 β + sin (α - β + α + β) sin (α - β - α - β)

= cos 2 α cos 2 β - sin 2 α sin 2 β

= cos (2 α + 2 β)

= RHS

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Question Text	Prove that : $cos 2 α cos 2 β + sin^{2} (α - β) - sin^{2} (α + β) = cos 2 (α + β)$
Answer Type	Text solution:1
Upvotes	150