Answer:
see explanation
Step-by-step explanation:
Using the identities
sin(A + B) = sinAcosB + cosAsinB
cotA = [tex]\frac{cosA}{sinA}[/tex] , tanA = [tex]\frac{sinA}{cosA}[/tex]
Consider the left side
[tex]\frac{sin(A+B)}{sinAcosB}[/tex]
= [tex]\frac{sinAcosB+cosAsinB}{sinAcosB}[/tex]
= [tex]\frac{sinAcosB}{sinAcosB}[/tex] + [tex]\frac{cosAsinB}{sinAcosB}[/tex]
= 1 + [tex]\frac{cosA}{sinA}[/tex] . [tex]\frac{sinB}{cosB}[/tex]
= 1 + cotA tanB = right side , thus verified
