Grade 11Trigonometry
If A+B+C =pie,then prove that ∑(tanA÷tanBtanC) = ∑(tanA) -2∑(cotA).
If A+B+C =pie,then prove that ∑(tanA÷tanBtanC) = ∑(tanA) -2∑(cotA).
1 Answer
Saurabh Koranglekar
Approved Tutor Answer7 Years agoA+B+C = 180 ;
A+B = 180 – C ;
/* take tangent on both sides and simplifiy
Tan A + Tan B + Tan C = (Tan A)*(Tan B)*(Tan C)
take LCM of LHS in expanded form */
(Tan 2A +Tan2B+Tan2C) ./ ((Tan A)*(Tan B)*(Tan C))
simplify using (a^2 + b^2 + c^2) = (a+b+c)^2 – 2(ab + bc + ca);
you will get RHS
A+B = 180 – C ;
/* take tangent on both sides and simplifiy
Tan A + Tan B + Tan C = (Tan A)*(Tan B)*(Tan C)
take LCM of LHS in expanded form */
(Tan 2A +Tan2B+Tan2C) ./ ((Tan A)*(Tan B)*(Tan C))
simplify using (a^2 + b^2 + c^2) = (a+b+c)^2 – 2(ab + bc + ca);
you will get RHS