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

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

Grade:10

3 Answers

Magnumaverick
25 Points
7 years ago
Taking cosine on both sides,we get
  • cos(A+B)=cos(π/2)
  • cosAcosB-sinAsinB=0
  • cosAcosB=sinAsinB
  • tanA=tanB
  • A=nπ+B
  • If n=0,
  • A=B--------1
LHS=tanA
      =tanB-------2  (BY 1)
RHS=tanB+2tan(A-B)
       =tanB +2tan(B-B)----By 1
        =tanB-------3
from 2 and 3,
LHS=RHS
HENCE PROVED!!!
Balaji
18 Points
7 years ago
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)
Balaji
18 Points
7 years ago
I am sorry for that poor formatting of my answer. Can anyone help me how to format the answer? [b]Does BB code work [/b]

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