Question

Find the value of 2tan30/1+tan2. 30

Answer 1

Answer:

tan2(30)/1+tan2(30)

tan60/1+tan60

√3/1+√3

After this use rationalisation

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Answer 2

$\red{Value \:of \: \frac{ 2tan 30 }{1 + tan^{2} 30\degree }}$

$= \frac{ 2\times \frac{1}{\sqrt{3}}}{ 1+ \Big( \frac{1}{\sqrt{3}}\Big)^{2}}$

$= \frac{ \frac{2}{\sqrt{3}}}{ \frac{ 3+1}{3}} \\= \frac{ 2}{\sqrt{3}} \times \frac{3}{4} \\= \frac{\sqrt{3}}{2}$

Therefore.,

$\red{Value \:of \: \frac{ 2tan 30 }{1 + tan^{2} 30\degree }}\green {= \frac{\sqrt{3}}{2} }$

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