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OpenStudy (anonymous):
If A+B+C=180 and cosA=cosB.cosC, then prove that tanB.tanC=2
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OpenStudy (solomonzelman):
A=180-(B+C) cosA = - cos(B+C) = - (cosB cosC - sinB sinC) = - cosB cosC + sinB sinC But cosA =cosB cos C. So, - cosb cosc + sinb sinc = cosb cos c and therefore sinb sinc = 2 cosb cosc Dividing through by cosb cosc we get tanb tanc = 2
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