Math, asked by lion49114, 9 months ago

cos^2(45-a)-sin^2(45-a)=sin2a​

Answers

Answered by rsingh625
12

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Using the addition identity for sine

sin(x + y) = sinxcosy - cosxsiny

Consider the left side

cos²(45 - A) - sin²(45 - A)

cos²(45 - A) = 1 - sin²(45 - A), thus

1 - sin²(45 - A) - sin²(45 - A)

= 1 - 2sin²(45 - A) ← expand sin(45 - A)

= 1 - 2(sin45cosA - cos45sinA)²

= 1 - 2(cosA - sinA)²

= 1 - 2(cos²A - sinAcosA + sin²A)

= 1 - cos²A + 2sinAcosA - sin²A

= sin²A + 2sinAcosA - sin²A

= 2sinAcosA

= sin2A = right side ⇒ verified

Answered by shahyansu23
7

Answer:

Hope its helpful

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