Question

if tan 15°=x the probe that
${x}^{2} + 2 \sqrt{3} x - 1$=0
​

Answer 1

$\Huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

$\Large{\sf{Given :}}$

Value of tan 15° = x

$\rule{200}{2}$

$\LARGE{\sf{To \: Find :}}$

⇒ x² + 2√3x - 1

$\rule{200}{2}$

$\LARGE{\sf{Solution :}}$

We know that,

$\LARGE{\boxed{\boxed{\green{\tt{tan \: 15 ^{\circ} \: = \: 2 - \sqrt{3}}}}}}$

(Putting Values)

$\sf{(2 - { \sqrt{3}) }^{2} + 2 \sqrt{3}(2 - \sqrt{3}) - 1 = 0 }$

Using Identity :-

$\large{\boxed{\boxed{\orange{(a - b)^2 = a^2 + b^2 + 2ab}}}}$

$⇒\sf{4 + 3 - \cancel{ 4 \sqrt{3} } + \cancel{4 \sqrt{3}} - 6 - 1 = 0} \\ \\ ⇒ \sf{ \cancel7 - \cancel7 = 0} \\ \\ ⇒ \sf{ 0= 0}$

$\Large{\boxed{\red{\sf{Hence \: proved}}}}$

Answer 2

Given :

$\bold \green{tan \: 15 \degree = x}$

We need to find the value of the equation

By using this ✓

We know

$\boxed{\boxed{\huge \blue{tan15 \degree = 2 - \sqrt{3}}}}$

So

$\boxed{\bold{x = 2 - \sqrt{3} }}$

So let out the value of X in the equation so as to find the value ✓

$= > x ^{2} + 2 \sqrt{3} -1 \\ \\ = > (2 - \sqrt{3} )^{2} + 2 \sqrt{3} (2 - \sqrt{3} ) - 1 \\ \\ = >2 ^{2} + (\sqrt{3} )^{2} - 2 \times 2 \sqrt{3} + 4 \sqrt{3} - 2 \times 3 - 1 \\ \\ = > 4 + 3 - 4 \sqrt{3} + 4 \sqrt{3} - 6 - 1 \\ \\ = > 7 - 7 \\ \\ = > 0$

$\boxed{\boxed{\red{\huge{hence \: proved}}}}$