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Question Number 17233 by sushmitak last updated on 02/Jul/17

$$\mathrm{How}\mathrm{to}\mathrm{find}\mathrm{out}\mathrm{if}$$ $$\cos \left(\cos x\right)>\sin \left(\sin x\right)$$ $$\cos \left(\sin x\right)>\sin \left(\cos x\right)$$ $$\cos \left(\sin \left(\cos x\right)\right)>\sin \left(\cos \left(\sin x\right)\right)$$ $$\cos \left(\cos \left(\cos x\right)\right)>\sin \left(\sin \left(\sin x\right)\right)$$ $$\mathrm{exam}\mathrm{questions}.$$ $$\mathrm{calculators}\mathrm{not}\mathrm{allowed}.$$

Commented byprakash jain last updated on 03/Jul/17

$$\mathrm{One}\mathrm{option}\mathrm{is}\mathrm{to}\mathrm{manually}\mathrm{check}$$ $$\mathrm{for}x\mathrm{from}0\mathrm{to}2\pi ,\mathrm{in}\mathrm{the}\mathrm{intervals}$$ $$\mathrm{for}\frac{\pi }{8}$$ $$0,\frac{\pi }{8},\frac{2\pi }{8},\frac{3\pi }{8},\frac{4\pi }{8},...,..\frac{16\pi }{8}$$ $$\mathrm{I}\mathrm{am}\mathrm{not}100\mathrm{\%}\mathrm{sure}.$$ $$\mathrm{but}\mathrm{Tinkutara}\mathrm{has}\mathrm{also}\mathrm{been}\mathrm{woking}$$ $$\mathrm{on}\mathrm{many}\mathrm{such}\mathrm{problem}\mathrm{he}\mathrm{may}$$ $$\mathrm{have}\mathrm{some}\mathrm{suggestion}.$$ $$\mathrm{mrW}1,\mathrm{ajfour}\mathrm{any}\mathrm{comments}?$$

Commented by1234Hello last updated on 03/Jul/17

$$\mathrm{Maybe}\mathrm{there}\mathrm{is}\mathrm{an}\mathrm{idea}:\mathrm{Range}\mathrm{of}$$ $$\cos \left(\cos x\right)\mathrm{is}[\cos 1,1]\mathrm{and}\mathrm{that}\mathrm{of}$$ $$\sin \left(\sin x\right)\mathrm{is}[-\sin 1,\sin 1]\mathrm{and}\mathrm{second}$$ $$\mathrm{is}\mathrm{the}\mathrm{graphical}\mathrm{method}.$$

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