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Show that f(x) = x/sin x is increasing on ]0, π/2[. |
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Answer» It is given that f(x) = x/sin x By differentiating w.r.t. x f’(x) = (sin x. 1 – x. cos x)/(sin x)2 = (sin x – x cos x)/(sin x)2 We know that f’(x) > 0 By substituting the values (sin x – x cos x)/(sin x)2 > 0 So we get (sin x – x cos x) > 0 Here tan x > x which is true on ] 0, π/2[. |
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