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Question

Let x=sin1 , then the value of the expression
1cos0.cos1+1cos1.cos2+1cos2.cos3+....+1cos44.cos45 is equal to

A
x
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B
1x
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C
2x
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D
x2
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Solution

The correct option is C 1x
Given x=sin1
1cos0cos1+1cos1cos2+1cos2cos3++1cos44cos45=1sin1(44r=0sin1cosrcos(r+1))
=1x(44r=0sin((r+1)r)cos(r+1)cosr)
=1x44r=0sin(r+1)cosrcos(r+1)sinrcos(r+1)cosr
=1x44r=0(tan(r+1)tanr)
=1x(tan1tan0+tan2tan1++tan45tan44)
=1x(tan45tan0)
=1x

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