sin of an angle in terms of cot x

\[\frac{1+sin2x+cos2x}{1+sin2x-cos2x}=cotx\]

=\frac{(1+cos2x)+sin2x}{(1-cos2x)+sin2x}\]

=\[\frac{2cos^2x+2sinx cosx}{2sin^2x+2sinxcosx}\]

=\[\frac{2cosx(cosx+ sinx)}{2sinx(sinx+cosx)}\]

=cotx=RHS

For x= 45 cot45=1

     x=30  cot30=\[ \sqrt{3}\]

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