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For 0ltxlt(pi)/(6), all the values of tan^(2)3x cos^(2)x-4tan3xsin2x+16sin^(2)x lie in the interval |
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Answer» `(0,(121)/(36))` `tan^(2)3x cos^(2)x-4tan3xdsin2x+16sin^2)x` `=((tan^(2)3x)/(tan^(2)x)-(8tan3x)/(tanx))sin^(2)x=((tan3x)/(tanx)-)^(2)sin^(2)x` We KNOWN that `1/3lt(tan3x)/(tanx)lt3` `implies-11/3lt(tan3x)/(tanx)-4lt-1implies1lt((tan3x)/(tanx)-4)^(2)lt(121)/(9)` Also, `0ltxlt(pi)/(9)implies0sinxlt1/2implies0ltsin^(2)xlt1/4` `therefore0lt((tan3x)/(tanx)-4)^(2)sin^(2)xlt(121)/(36)` |
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