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Let $a_{1} = \cos (\sin πx), a_{2} = \sin (\cos πx)$ and $a_{3} = \cos (π (x + 1)), where - \frac{1}{2} < x < 0$ .What are the relative sizes of $a_{1}, a_{2} and a_{3}$ ?

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detailed solution

Correct option is A

Let y = - x, then we have 00,a2=sin⁡(cos⁡πy)>0 and a3=cos⁡(1−y)π=−cos⁡πy<0now, sin⁡πy+cos⁡πy≤2<π2⇒sin⁡(cos⁡πy)

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Let a1=cos⁡(sin⁡πx),a2=sin⁡(cos⁡πx) and a3=cos⁡(π(x+1)), where −12<x<0 .What are the relative sizes of a1,a2 and a3 ?

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Let $a_{1} = \cos (\sin πx), a_{2} = \sin (\cos πx)$ and $a_{3} = \cos (π (x + 1)), where - \frac{1}{2} < x < 0$ .What are the relative sizes of $a_{1}, a_{2} and a_{3}$ ?