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?
Venkata Ramana , 8 Years ago
Grade 10
Trigonometry> if A+B= π/2 , prove that tanA=tanB +2 tan...
3 Answers
Magnumaverick
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
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
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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