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Question

If α is only real root of the equation x3(cos1)x2+(sin1)x+1=0, then (tan1α+tan11α) cannot be equal to _____________.

A
0
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B
π2
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C
π2
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D
π
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Solution

The correct options are
A 0
B π2
D π
Let f(x)=x3+(cos1)x2+(sin1)x+1
f(0)=1
f()=
If α<0tan1α<0
tan1(1α)<0
tan1α+tan1(1α)<0 and cannot be equal to for α=0
tan1α+tan1(1α)<0 and cannot be equal to for α=π2
tan1α+tan1(1α)<0 and cannot be equal to for α=π
Option (a),(b) and (d) are the correct answers.




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