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Question

Sin(A+B)+sin(A+B)/Cos(A+B)+cos(A-B)=TanA


Solution

Expand the given formula by Sin(A+B)=sinAcosB+cosAsinB
sin(A-B)= sinAcosB-cosAsinB
cos (A-B)=cosAcosB+sinAsinB
cos (A+B)=cosAcosB-sinAsinB
 =[(sinAcosB+cosAsinB) + (sinAcosB-cosAsinB)] /[(cosAcosB-sinAsinB) + (cosAcosB+sinAsinB)]

=2sinAcosB / 2cosAcosB

=sinA/cosA= tanA
hence proved

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