Trigonometry..

IIT JEE Discussion Forum › Olympiad Stuff questions › Trigonometry..

In a \Delta ABC, let

x=\tan\left(\frac{B-C}{2}\right)\tan\left(\frac{A}{2}\right)

y =\tan\left(\frac{C-A}{2}\right)\tan\left(\frac{B}{2}\right)

z =\tan\left(\frac{A-B}{2}\right)\tan\left(\frac{C}{2}\right)

Prove that x+y+z+xyz = 0

#Mathematics #Olympiad Stuff

UP 0 DOWN 0 0 2
Post on FacebookPost anonymously?

2 Answers

aieeee ·2009-07-26 21:04:30

ACTUALLY,its a formula,which goes this way: tan(B-C/2) = b-c/b+c hope,u cn solve it now.

( derirvation of the formula:

b-c/b+c = sinB-sinC/sinB+sinC ,
= (2 sin B-C/2 *cos B+C/2) / ( 2 sin B+C/2*cos B-C/2)
= (tan B-C/2) / (tan B+C/2)
now,putting B+C=âˆ© - A, U GET THE FORMULA

UP 0 DOWN 0
Post on FacebookPost anonymously?

Devil ·2009-07-27 06:51:45

Napier's Analogy....

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

Close [X]

Trigonometry..

2 Answers

Your Answer

Add Image

Similar Questions