Prove $cos^{2} α - sin^{2} 2 α = cos^{2} α cos 2 α - 2 sin^{2} α cos^{2} α .$

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Prove

cos^{2} α - sin^{2} 2 α = cos^{2} α cos 2 α - 2 sin^{2} α cos^{2} α .

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= cos^{2} α - sin^{2} α

= cos^{2} α - 4 sin^{2} α cos^{2} α [∵ sin 2 α = 2 sin α cos α]

= cos^{2} α - 2 sin^{2} α cos^{2} α - 2 sin^{2} α cos^{2} α

= cos^{2} α [1 - 2 sin^{2} α] - 2 sin^{2} α cos^{2} α

= cos^{2} α cos 2 α - 2 sin^{2} α cos^{2} α

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Question Text	Prove $cos^{2} α - sin^{2} 2 α = cos^{2} α cos 2 α - 2 sin^{2} α cos^{2} α .$
Answer Type	Text solution:1
Upvotes	150