Prove the Following Identity : Sin 2 a Cos 2 B − Cos 2 a Sin 2 B = Sin 2 a − Sin 2 B - Mathematics

Question

Prove the following identity :

$\sin^{2} A \cos^{2} B - \cos^{2} A \sin^{2} B = \sin^{2} A - \sin^{2} B$

Sum

Solution

LHS = $\sin^{2} A (1 - \sin^{2} B) - (1 - \sin^{2} A) \sin^{2} B$

= $\sin^{2} A - \sin^{2} A . \sin^{2} B - \sin^{2} B + \sin^{2} A . \sin^{2} B$

= $\sin^{2} A - \sin^{2} B$ = RHS

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Trigonometric Identities

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Q 2.01 Q 1.13 Q 2.02

Chapter 21: Trigonometric Identities - Exercise 21.1

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Chapter 21 Trigonometric Identities
Exercise 21.1 | Q 2.01

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Prove the Following Identity : Sin 2 a Cos 2 B − Cos 2 a Sin 2 B = Sin 2 a − Sin 2 B - Mathematics

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Prove the Following Identity : Sin 2 a Cos 2 B − Cos 2 a Sin 2 B = Sin 2 a − Sin 2 B - Mathematics

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