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Question

Number of solutions to the equation
tan1(1x1+1x2+1x3+1x4)+cos1(x)=3π4sin1(x) are

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is B 2
Given,
tan1(1x1+1x2+1x3+1x4)+cos1(x)=3π4sin1x

tan1(1x1+1x2+1x3+1x4)+cos1(x)=π4+π2sin1x

tan1(1x1+1x2+1x3+1x4)+cos1(x)=π4+cos1x

tan1(1x1+1x2+1x3+1x4)=π4

(1x1+1x2+1x3+1x4)=tan(π4)

(1x1+1x2+1x3+1x4)=1

4x10(x1)(x2)(x3)(x4)=1

4x10=(x1)(x2)(x3)(x4)

Hence the number of solution of x=2

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