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trigonometric identity..... isi 2012 #1

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May 13, 2012
trigonometry

Problem Statement

i)If X,Y,ZX,Y,Z be the angles of a triangle then show that tan⁡X2tan⁡Y2+tan⁡Y2tan⁡Z2+tan⁡Z2tan⁡X2=1\tan {\frac{X}{2}}\tan {\frac{Y}{2}}+\tan {\frac{Y}{2}}\tan {\frac{Z}{2}}+\tan {\frac{Z}{2}}\tan {\frac{X}{2}}=1 ii) Prove using (i) or otherwise that tan⁡X2tan⁡Y2tan⁡Z2≤133\tan {\frac{X}{2}}\tan {\frac{Y}{2}}\tan {\frac{Z}{2}}\leq\frac {1}{3\sqrt{3}}
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