F.4 TRIGONOMETRY M2!!

tanA + tanB

= sinA/cosA + sinB/cosB

= (sinAcosB + cosAsinB)/(cosAcosB)

= sin(A + B)/(cosAcosB)

cotA + cotB

= cosA/sinA + cosB/sinB

= (cosAsinB + sinAcosB)/(sinAsinB)

= sin(A + B)/(sinAsinB)

(tanA + tanB)/(cotA + cotB)

= [sin(A + B)/(cosAcosB)]/[sin(A + B)/(sinAsinB)]

= tanAtanB

(tan A + tan B)/(cot A + cot B)
= (tan A + tan B)/( 1/tan A + 1/tan B)
= (tan A + tan B)/[(tan A + tan B)/(tan A tan B)]
=tan A tan B.