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Question

If cos3xcosx=13 for some angle 0<x<π2, then the value of sin3xsinx for same x, is

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Solution

Consider, sin3xsinxcos3xcosx
=sin3xcosxcos3xsinxsinxcosx=sin2xsinxcosx=2sin2xsin2x=2
So,sin3xsinx13=2
sin3xsinx=2+13=73

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