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If `y=(sin^4x-cos^4x+sin^2xcos^2x)/(sin^4x+cos^4x+sin^2xcos^2x),x in (0,pi/2)`, then`-3/2lt=ylt=1/2`(b) `1lt=ylt=1/2``-5/3lt=y1`(d) none of theseA. `-(3)/(2)le y le (1)/(2)`B. `(1)/(2)le y le 1`C. `-(5)/(3)le y le 1`D. `-1le y le 1` |
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Answer» Correct Answer - D `y = (sin^(4)x-cos^(4)x+sin^(2)x cos^(2)x)/(sin^(4)x +cos^(4)x +sin^(2)x cos^(2)x cos^(2)x)` `y = (- cos2x+(1)/(4)sin^(2)2x)/(1-(1)/(4)sin^(2)2x)` `= (1-4cos2x- cos^(2)2x)/(3+cos^(2)2x)` `(1+y)cos^(2)2x+4cos2x+3y-1=0` `D ge 0` `-(5)/(3) le y le 1` but when `y = 1` `x = (pi)/(2)` which is not permissible |
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