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Question Number 55908 by gunawan last updated on 06/Mar/19

$$\mathrm{known}a<\frac{\pi }{2}.$$ $$\mathrm{If}\mathrm{M}<1\mathrm{with}\mid \cos x-\cos y\mid ⩽\mathrm{M}\mid x-y\mid$$ $$\mathrm{for}\mathrm{every}x,y\in [0,a],\mathrm{then}\mathrm{M}=..$$

Answered by tanmay.chaudhury50@gmail.com last updated on 07/Mar/19

$$lety>x$$ $$socosx>cosy$$ $$=cosx-cosy$$ $$=+ve$$ $$butx-y=-ve$$ $$\mid x-y\mid =+ve$$ $$fromattachedgraph$$ $$tan\theta =\frac{y_2-y_1}{x_2-x_1}=\frac{cosy-cosx}{y-x}$$ $$tan\theta =M=\frac{cosy-cosx}{y-x}butcosx>cosy$$ $$y>xsotan\theta =Mis-ve$$ $$wait...$$

Commented bytanmay.chaudhury50@gmail.com last updated on 07/Mar/19

Commented bygunawan last updated on 07/Mar/19

$$\mathrm{What}\mathrm{is}\mathrm{the}+ve\mathrm{Sir}?$$ $$$$

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