Question

Esin (A+B). Sin (A-B) solution
​

Answer 1

Question

To find sin(A + B).sin(A - B)

Answer:

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

Step-by-step explanation:

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

= (sinAcosB + cosAsinB)(sinAcosB - cosAsinB)

= (sinAcosB)² - (cosAsinB)²

= sin²Acos²B - cos²Asin²B

= sin²A(1 - sin²B) - (1 - sin²A)sin²B

= sin²A - sin²Asin²B - sin²B + sin²Asin²B

= sin²A - sin²B

Answer 2

Given

$Sin(A+B) . Sin (A-B)$

Solving, we get

$sin(A + B).sin(A - B)\\= (sinAcosB + cosAsinB)(sinAcosB - cosAsinB)\\= (sinAcosB)^{2} - (cosAsinB)^{2} \\= sin^{2} Acos^{2} B - cos^{2} Asin^{2} B\\= sin^{2} A(1 - sin^{2} B) - (1 - sin^{2} A)sin^{2} B\\= sin^{2} A - sin^{2} A \ sin^{2} B - sin^{2} B + sin^{2} A \ sin^{2} B\\=\boxed{\boxed{\bold{ sin^{2} A - sin^{2} B}}}}$