appl of derivatives

1 Answers

sin x / x < sin (sin x) / sin x

we just have to prove that sin x / x is a

f(x) = sin x / x

just proving that f(x) is decreasing in interval (0,1) will prove this !!!

cos x / x - sin x / x² = (x cos x - sin x)/x²

so prve that x cos x - sin x < 0 for 0 < x <1

which is true because

derivative of this is - x sin x <0 for 0<x<1

hence the above is proved

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