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  • If cot x = 1/root(3). Show that sin^2 x /(1+cos^2 x)=3/5

If cot x = 1/root(3). Show that sin^2 x /(1+cos^2 x)=3/5

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Divide the numerator and denominator by sin2x

\\\frac{sin^2x}{1+cos^2x}=\frac{1}{cosec^2x+cot^2x}\\\\=\frac{1}{1+cot^2x+cot^2x}=\frac{1}{1+2cot^2x}\\\\=\frac{1}{1+2\times(\frac{1}{\sqrt{3}})^2}=\frac{1}{1+\frac{2}{3}}=\frac{3}{5}

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Safeer PP

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