Question

Choose the correct option :

2tan30 /(1-tan^230) =

I) tan 90
ii) cot 30
iii) tan 60
iv) cot 45​

Answer 1

Hi mate

➡️2 tan 30/(1+tan^2 30)

➡️2(1√3)/(sec^2 30)

➡️2/√3/(2/√3^2)

➡️2/√3/(4/3)

➡️√3/2= cos 30

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Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

CORRECT ANSWER :

(III) Tan 60°

EXPLANATION :

$= \: \frac{ 2 \: tan \: 30 \degree }{1 - {tan}^{2}30 \degree }$

Putting the value of tan 30°, we get

$= \: \frac{2( \frac{1}{ \sqrt{3} } )}{1 - ({ \frac{1}{ \sqrt{3} } )}^{2} }$

$= \: \frac{ \frac{2}{ \sqrt{3} } }{1 - \frac{1}{3} }$

$= \: \frac{ \frac{2}{ \sqrt{3} } }{ \frac{2}{3} }$

$= \: \frac{2}{ \sqrt{3} } \times \: \frac{3}{2}$

$= \: \frac{3}{ \sqrt{3} }$

Multiplying √3 in both numerator and denominator,

$= \: \frac{3 \sqrt{3} }{3}$

Cancelling 3, we get

$= \: \sqrt{3}$

$= \: tan \: 60 \degree$

So, we got the given option (iii) tan 60° as correct.