Anonymous

# Cos(A+B)cos(A-B) = cos^2 -sin^2B please show the workings in all areas for best answer?

Update:

Sorry. It is supposed to equal cos^2A - sin^2B

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- 2 years agoFavorite Answer
LHS = cos(A+B) cos( A-B)

=(cosAcosB - sinAsinB)(cosAcosB + sinAsinB)

= (cosA cosB)² - (sinA sinB)²

= cos²A cos²B - sin²A sin²B

=cos²A ( 1-sin²B) - (1 - cos²A) sin²B

=( cos ²A - cos²A sin ²B) - (sin²B - cos²A sin²B)

= cos² A - sin²B = RHS .......proved

Source(s): Note : • cos(A+B) = (cosAcosB - sinAsinB) • cos(A-B) = (cosAcosB + sinAsinB) • (x - y)(x + y) = x² - y² • cos²B = 1 - sin²B • sin²A = 1 - cos²A - ted sLv 72 years ago
comment : won't equal what you typed !!....uses the concept of ( x - y ) ( x + y ) = x² - y² where x = cos A cos B and y = sin A sin B.... as well as cos² Θ + sin² Θ = 1 ....try it

- Anonymous2 years ago
Answer is 20

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