InterviewSolution
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InterviewSolution
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In ` A B C ,s i d e sb , c`and angle `B`are given such that `a`has two valus `a_1a n da_2dot`Then prove that `|a_1-a_2|=2sqrt(b^2-c^2sin^2B)` |
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Answer» `cos B = (c^(2) + a^(2) - b^(2))/(2ca)` or `a^(2) - (2c cos B) a + c^(2) - b^(2) = 0` This equation has roots `a_(1) and a_(2)` `rArr a_(1) + a_(2) = 2c cos B, a_(1) a_(2) = c^(2) - b^(2)` `rArr (a_(1) -a_(2))^(2) = (a_(1) + a_(2))^(2) - 4a_(1) a_(2) = 4c^(2) cos^(2) B - 4(c^(2) - b^(2))` `= 4b^(2) - 4c^(2) sin^(2) B = 4(b^(2) -c^(2) sin^(2) B)` or `|a_(1) -a_(2)| = 2 sqrt(b^(2) - c^(2) sin^(2) B)` |
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