if A+B=π/2 , prove that tanA=tanB+2 tan(A-B) and hence deduce that tan 55 = tan 35 + tan 20?

• cos(A+B)=cos(π/2)
• cosAcosB-sinAsinB=0
• cosAcosB=sinAsinB
• tanA=tanB
• A=nπ+B
• If n=0,
• A=B--------1

tan(a+b)=(tan a + tan b)÷(1-tanA.tanB). Since a+b= π/2, tan(a+b) will be of the form 1/0. So equating denominator to 0, we get tanAtanB=1.Now take tan(A-B)= (tan A - tan B)÷(1+tanA tanB)Here put tanAtanB=2So tan(A-B)=(1/2)*(tan A-tanB)Rearranging the terms,tan A=tanB + 2tan(A-B)

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