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)
