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Question

IfnN,nk=1Sin1(xk)=nπ2thennk=1xk=

A
n
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B
k
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C
k(k+1)2
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D
n(n+1)2
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Solution

The correct option is A n

nk=1sin1(xk)=(nπ2)sin1x1+sin1x2+.........+sin1xn=(nπ2)asmeanvalueofsin1x=(π2)forLHS=RHSvalueofeachsininversetermshouldbeequalto(π2)nowsin1x1=sin1x2=.........=sin1xn=(π2)x1=1,x2=1,x3=1,.........,xn=1thennk=1xk=nk=11=n


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