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Question

The product of all values of x satisfying the equation sin1cos(2x2+10|x|+4x2+5|x|+3)=cot(cot1(218|x|9|x|))+π2 is

A
9
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B
9
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C
3
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D
1
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Solution

The correct option is A 9
sin1cos(2x2+10|x|+4x2+5|x|+3)=cot(cot1(218|x|9|x|))+π2(π2sin1cos(2x2+10|x|+4x2+5|x|+3))=218|x|9|x|cos1cos(2x2+10|x|+62x2+5|x|+3)=29|x|18|x|9|x|2(x2+5|x|+3)(x2+5|x|+3)+2(x2+5|x|+3)=29|x|2or,9|x|=x2+5|x|+3[Assumingx0]x2+4|x|+3=0x23|x||x|+3=0(|x|3)(|x|1)=0|x|=3or,|x|=1x=3,3&x=1,1
Product of all real value =3×(3)×1×(1)=9

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