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Question

The numerical value of (1+cotxcosec x)(1+tanx+secx) is

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Solution

(1+cotxcosec x)(1+tanx+secx)=(1+cosxsinx1sinx)(1+sinxcosx+1cosx)=(sinx+cosx1sinx)(sinx+cosx+1cosx)=(sinx+cosx)21sinxcosx=sin2x+cos2x+2sinxcosx1sinxcosx=2sinxcosxsinxcosx=2

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