Question

prove thatprove that
(1+tan15°)(1+tan30°)=2

Answer 1

To prove:-

$\bf (1+tan15°)(1+tan30°)=2$

Proof:-

We know that

$\boxed{\bf 15°+30°=45°}$

$\sf{:}\implies tan (15°+30°)=tan45°$

$\sf{:}\implies \dfrac {tan15°+tan30°}{1-tan15°.tan30°}=1$

$\sf{:}\implies tan15°+tan30°=1-tan15°.tan30°$

$\sf{:}\implies tan15°+tan30°+tan15°.tan30°=1$

$\sf{:}\implies 1+tan15°+tan30°+tan15°.tan30°=1+1$

$\sf{:}\implies 1+tan15°+tan30°+tan15°.tan30°=2$

$\sf{:}\implies 1 (1+tan15°)+tan30°(1+tan15°)=2$

$\sf{:}\implies (1+tan15°)(1+tan30°)=2$

$\therefore{\huge{ \bf{(Proved)}}}$