InterviewSolution
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InterviewSolution
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In a `Delta ABC " if " |(1,a,b),(1,c,a),(1,b,c)| =0`, then `sin^(2) A + sin^(2) B + sin^(2) C` isA. `(9)/(4)`B. `(4)/(9)`C. `(3 sqrt3)/(2)`D. 1 |
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Answer» Correct Answer - A We have, `|(1,a,b),(1,c,a),(1,b,c)| =0` `rArr a^(2) + b^(2) + c^(2) - ab - bc - ca = 0` `rArr (1)/(2) {(a -b)^(2) + (b-c)^(2) + (c -a)^(2)} = 0` `rArr a - b = 0, b -c =0, c -a = 0 rArr a = b = c` `rArr Delta ABC` is equilateral `rArr A = B = C = pi//3` `:. sin^(2) A + sin^(2) B + sin^(2) C = (3)/(4) + (3)/(4) + (3)/(4) = (9)/(4)` |
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