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Find the range of `f(x)=sqrt(sin(cos x))+sqrt(cos(sin x))`. |
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Answer» `f(x)=sqrt(cos(sinx))+sqrt(sin(cosx))` Period of `f(x)` is `2 pi`. Also, `sin(cosx) ge 0 impliescosx in [0,1]` `implies x in [-(pi)/(2),(pi)/(2)]` ` :. x` lies in `1^(st)` and `4^(th)` quadrants. Also `f(-x)=f(x)` ` :. f(x)` is even. ` :. ` we need to find the range in `[0,(pi)/(2)]` only In `[0,(pi)/(2)], sinx` increases, but `cosx` decreases ` :. " both " cos(sinx) and sin(cosx)` decrease. Hence `f(x)` decreases, ` :. ` Range is `[f(pi//2),f(0)] -=[sqrt(cos 1),1+sqrt(sin1)]` |
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