Question

Prove it..
1.sin²A.cos²Bsin²B=sin²A-sin²B

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Answer 1

Answer:

sin(A+B)sin(A--B)

= (sinAcosB+cosAsinB)(sinAcosB--cosAsinB)

= (sinAcosB)^2 -- (cosAsinB)^2

= sin^2A(1--sin^2B) --sin^2B(1--sin^2A)

= sin^2A -- sin^2Asin^2B -- sin^2B + sin^2Asin^2B

= sin^2A -- sin^2B