InterviewSolution
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Let f(sin x)lt 0and f(sin x) lt 0for all x in |
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Answer» `(pi/4,pi/2)` `rArrg(x)=f'(sin x) cos^2 x+f' (cos x) sin ^2X -f(sin x)sin x-f(cos x) cos x` `rArrg'(x) gt 0 " for all " x in (0,pi//2)` Also `g(pi/4)=1/(sqrt(2))f((1)/(sqrt(2)))-(1/sqrt(2))f(1/sqrt(2))=0` `thereforeg(x) lt ` 0 for all `x in (0,pi/4)` and `g(x) gt 0 ` for all `x in (pi/4,Pi/2)` `rArrg(x)` is decreasing on `(0,pi/4)` and increasing on `(pi/,pi/2)` |
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