Cos^2B-sin^2A/(sin A cos A + sin B cos B) = cot (A + B)​

Step-by-step explanation:

Compound angle formula:

sin(A + B)=sinAcosB+cosAsinB

cos(A - B)=cosAcosB+sinAsinB

nominator:

(cos^2B-sin^2A)

=cos^2B-(cos^2B)(sin^2A)-sin^2A+(cos^2B)(sin^2A)

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

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

=[(cosB)(cosA)]^2-[(sinA)(sinB)]^2

=(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)

=cos(A + B)cos(A - B)

denominator:

(sin A cos A + sin B cos B)=sin(A + B) cos(A - B)

cos^2B-sin^2A/(sin A cos A + sin B cos B)

=[cos(A + B)cos(A - B)] / [sin(A + B) cos(A - B)]

=cos(A + B)/sin(A + B)

=1/tan(A+B)

=cot(A+B)

answer: ouch. thats difficult

step-by-step explanation: