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Ask iit jee aieee pet cbse icse state board community Discussion Response Post to: sinA,cosA and tanA are in G.P. the Cot^6A-cot^2A is = to
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[Post New] 20 Jan 2009 12:37:55 IST
   Subject: sinA,cosA and tanA are in G.P. the Cot^6A-cot^2A is = to
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akki ~~ unlucky forever ~~ (1635)

Olaaa!! Perrrfect answer. 275  [405 rates]
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by conditions of GM

cos2A=sinAtanA

\frac{sin^2A}{cos^3A}=1    ......(i)

\frac{1}{cosA}(\frac{1}{cos^2A}-1)=1

\frac{cos^2A}{cos^3A}(\frac{cos^4A}{cos^6A}-1)=1

\frac{cos^2A}{sin^2A}(\frac{cos^4A}{sin^4A}-1)=1         ......(from (i))

cot^2A(cot^4A-1)=1

(cot^6A-cot^2A)=1
all's well that end's well, but if it dosen't, then it is not the end . . .
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