Question

sin (A+B).sin(A-B)=sin²A-sin²B​

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

Step-by-step explanation:

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Answer 2

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

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