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Cot theta=2n^2+2mn/m^2+2mn then prove cosec theta=m^2+2mn+2n^2/m^2+2mn

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$\cot \theta=\frac{2n^2+2mn}{m^2+2mn} \\\\ \csc \theta= \sqrt{1+ \cot^2 \theta } \\\\ \csc \theta= \sqrt{1+ (\frac{2n^2+2mn}{m^2+2mn})^2 }\\\\ = \frac{\sqrt{m^4+4m^2n^2 + 4m^3n+ 4n^4+4m^2n^2+ 8mn^3}}{m^2+2mn} \\\\ =\frac{\sqrt{(m^2 + 2n^2 + 2mn)^2}}{m^2+2mn}\\\\ =\frac{m^2+2mn+2n^2}{m^2+2mn}$

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Ravindra Pindel

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