Question

without using tables, prove that : (2 multiplied by 30 degree) = 1-tan^2 30 degree/ 1+ tan^2 30

Answer 1

$\huge\boxed{\fcolorbox{purple}{pink}{Answer:-}}$

It is given that,



sin ( 2 × 30° ) =

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



Taking the right hand side ,

$\frac{2 \: tan \: 30}{1 + tan ^{2} 30}$

=

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

$\frac{2}{ \sqrt{3} } \times \frac{3}{4} \\ \\ \frac{ \sqrt{3} }{2}$

= sin 60°

Hope this helps_♡