Question

(1+tanA.tanB)+tanA-tanB =secA.secB

Answer 1

(1+tanA.tanB) + tanA - tanB =secA.secB
-> 1+ (sinA.sinB)/cosA.cosB +sinA/cosA -sinA/cosA
-> (cosA.cosB+sinA.sinB)/(cosA.cosB) + (sinAcosB-sinBcosA)/(cosAcosB)

--> {cos(A-B)+sin(A-B)}/(cosAcosB)

--> {sin(pie/2 -(A-B)) + sin (A-B) } / (cosAcosB)

--> { 2sin( (pie/2-(A-B)+(A+B) )/2)cos( (pie/2- (A-B)+(A+B)/2) } /(cosAcosB)
--> { 2sin(pie/4)cos(pie/4) }/ (cosAcosB)

--> secA.secB