Question

2 tan 30°/
1 + tan^2 30°​

Answer 1

QUESTION:

$\frac{2 \tan(30) }{1 + { { \tan}^{2} 30 }$

ANSWER:

We use the trigonometry identity to solve the question :

$1 + { \tan( \alpha ) }^{2} = { \sec( \alpha ) }^{2}$

we know that

$\tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) }$

$\sec( \alpha ) = \frac{1}{ \cos( \alpha ) }$

NOW COME TO YOUR QUESTION :

$\frac{2 \times \frac{ \sin(30) }{ \cos( \alpha ) } }{ \frac{1}{ { \cos }^{2} 30} }$

$\frac{2 \times \sin(30) \times { \cos}^{2} 30}{ \cos(30) }$

$2 \times \sin(30) \times \cos(30)$

NOW,

$2 \times \frac{1}{2} \times \frac{ \sqrt{3} }{2} \\ \frac{ \sqrt{3} }{2}$

FINAL ANSWER :

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

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Answer 2

Step-by-step explanation:

QUESTION:

\frac{2 \tan(30) }{1 + { { \tan}^{2} 30 }

ANSWER:

We use the trigonometry identity to solve the question :

1 + { \tan( \alpha ) }^{2} = { \sec( \alpha ) }^{2}1+tan(α)

2

=sec(α)

2

we know that

\tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) }tan(α)=

cos(α)

sin(α)

\sec( \alpha ) = \frac{1}{ \cos( \alpha ) }sec(α)=

cos(α)

1

NOW COME TO YOUR QUESTION :

\frac{2 \times \frac{ \sin(30) }{ \cos( \alpha ) } }{ \frac{1}{ { \cos }^{2} 30} }

cos

2

30

1

2×

cos(α)

sin(30)

\frac{2 \times \sin(30) \times { \cos}^{2} 30}{ \cos(30) }

cos(30)

2×sin(30)×cos

2

30

\begin{gathered}2 \times \sin(30) \times \cos(30) \\ \end{gathered}

2×sin(30)×cos(30)

NOW,

\begin{gathered}2 \times \frac{1}{2} \times \frac{ \sqrt{3} }{2} \\ \frac{ \sqrt{3} }{2} \end{gathered}

2×

2

1

×

2

3

2

3

FINAL ANSWER :

\frac{ \sqrt{3} }{2}

2

3