Question

if A+B=45° then show that tanA+tanB+tanAtanB=1

Answer 1

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Answer 2

Step-by-step explanation:

A+B= 45

A=45-B

tanA=tan(45-B)

tanA=tan45-tanB/1+tan45tanB

tanA=1-tanB/1+tanB

LHS = tanA+tanB+tanAtanB

= 1-tanB/1+tanB + tanB + [1-tanB/1+tanB]tanB

= 1-tanB/1+tanB + tanB + tanB-tan²B/1+tanB

taking the LCM

= [1-tanB+tanB+tan²B+tanB-tan²B]/1+tanB

= 1+tanB/1+tanB

= 1 = RHS

Hence Proved