Question

(1+tan 15°)(1-tan 30°)=2 proved that

Answer 1

Answer:

$tan15 = \tan(45 - 30) = \frac{tan45 - tan30}{1 + tan45.tan30} = \frac{1 - \frac{1}{ \sqrt{3} } }{1 + \frac{1}{ \sqrt{3} } } = \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1}$

LHS,

$(1 + \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } )(1 + \frac{1}{ \sqrt{3} } ) =$

$( \frac{ \sqrt{3} + 1 + \sqrt{3} - 1}{ \sqrt{3} + 1 } )( \frac{ \sqrt{3} + 1 }{ \sqrt{3} } ) =$

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

RHS