Question

For any two real numbers A, B cos (A+B) cos (A-B) =
pls tell fast!​

Answer 1

For any two real numbers A and B,

we have to find cos(A + B). cos(A - B)

solution : we know from addition and subtraction formula,

cos(A + B) = cosA . cosB - sinA . sinB .......(1)

and cos(A - B) = cosA. cosB + sinA . sinB .....(2)

now cos(A + B) . cos(A - B) = {cosA . cosB - sinA . sinB}{cosA . cosB + sinA . sinB}

[ from equations (1) and (2) ]

= cos²A cos²B - sin²A sin²B

= (1 - sin²A)(1 - sin²B) - sin²A sin²B

= 1 - sin²B - sin²A + sin²A sin²B - sin²A sin²B

= (1 - sin²B) - sin²A

= cos²B - sin²A

Therefore the cos(A + B) . cos(A - B) = cos²B - sin²A