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Question

If 0<cos1x<1 and 1+sin(cos1x)+sin2(cos1x)+sin3(cos1x)+=2, then the value of 12x2 is

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Solution

1+sin(cos1x)+sin2(cos1x)+...=2
11sin(cos1x)=2
or 12=1sin(cos1x)
or sin(cos1x)=12 or cos1x=π6
or x=32 or 12x2=9

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