InterviewSolution
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InterviewSolution
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The equation `sin^4x-2cos^2x+a^2=0`can be solved if`-sqrt(3)lt=alt=sqrt(3)`(b) `sqrt(2)lt=alt=""sqrt(2)``-""1lt=alt=a`(d) none of theseA. `-sqrt(3) le a le sqrt(3)`B. `-sqrt(2) le a le sqrt(2)`C. `-1 le a le 1`D. none of these |
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Answer» Correct Answer - B We have `sin^(4) x-2 cos^(2) x+a^(2)=0` `:. a^(2)=2 cos^(2) x- sin^(4) x` `=2-2 sin^(2) x-sin^(4) x` `=3-(sin^(2) x+1)^(2)` Now `0 le sin^(2) x le 1` `:. 1 le sin^(2) x + 1 le 2` `:. 1 le (sin^(2) x+1)^(2) le 4` `:. -4 le -(sin^(2) x+1)^(2) le -1` `:. -1 le 3 -(sin^(2) x+1)^(2) le 2` `:. a^(2) le 2` `:. -sqrt(2) le a le sqrt(2)` |
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