InterviewSolution
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InterviewSolution
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Solve the inequality `sin2x gtsqrt(2)sin^2x+(2-sqrt(2))cos^2x` |
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Answer» Correct Answer - `x in (n pi +pi/8, n pi+pi/4), n in Z` `sin 2x gt sqrt(2) sin^(2) x+(2 -sqrt(2)) cos^(2)x` `rArr 2 sin x cos x gt sqrt(2) sin^(2) x+(2-sqrt(2))cos^(2) x` `rArr tan^(2)x-sqrt(2) tan x+(sqrt(2)-1) lt 0` `rArr (tan x-1) (tan x-(sqrt(2)-1)) lt 0` `rArr (sqrt(2)-1) lt tan x lt 1` `rArr pi//8 lt x lt pi//4` `:. x in (n pi + pi/8, n pi +pi/4)` where `n in Z`. |
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