InterviewSolution
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InterviewSolution
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If `C = 2 cos theta`, then the value of the determinant `Delta = |(C,1,0),(1,C,1),(6,1,c)|`, isA. `(sin 4 theta)/(sin theta)`B. `(2 sin^(2) 2 theta)/(sin theta)`C. `4 cos^(2) theta (2 cos theta -1)`D. none of these |
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Answer» Correct Answer - D We have, `Delta = |(C,1,0),(1,C,1),(6,1,c)|` `rArr Delta = |(0,1,0),(1 -C^(2),C,1),(6-C,1,C)| " " ["Applying " C_(1) rarr C_(1) - C C_(2)]` `rArr Delta = -|(1 -C^(2),1,),(6 -C,C,)|` [Expanding along `R_(1)`] `rArr Delta = - (C -C^(3) - 6 + C)` `rArr Delta = C^(3) - 2C + 6` `rArr Delta = 8 cos^(3) theta - 4 cos theta + 6` Hence, option (d) is correct |
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