Find the value of the following:
${tan}^{2} 60^{o} + 2 {tan}^{2} 45^{o}$

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Solution

We have, $tan 60^{o} = \sqrt{3}$ and $tan 45^{o} = 1$
$∴ {tan}^{2} 60^{o} + 2 {tan}^{2} 45^{o}$
$= {(\sqrt{3})}^{2} + 2 \cdot {(1)}^{2}$
$= 3 + 2 = 5$

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