In a triangle ABC, points D and E are taken on side BC such that BD = DE = EC. If angle
ADE = angle AED = θ , then:
= tan A
Text Solution
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(a,c,d)
if we apply m-n Rule in Δ ABE, we get
(1+1) cot θ = 1.cot B – 1.cot θ
2 cot θ = cot B – cot θ
3 cot θ = cot B
tan θ = 3 tan B ..........(1)
Similarly, if we apply m-n Rule in Δ ACD, we get
(1+1) cot ( π – θ ) = 1.cot θ – 1.cotC.
cotC = 3 cot θ ⇒ tan θ = 3 tanC .......(2)
form (1) and (2) we can say that
tan B = tan C ⇒ B=C
A + B + C = π
∴ A = π – (B + C)
= π – 2B 
B = C
∴ tan A = – tan2B
= – 
= – 
⇒ tan A = 
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