Question

tan 36° + tan9° + tan36° tan9°=1​

Answer 1

Step-by-step explanation:

We know that tan(A+B)=(tanA+tanB)/(1-tanAtanB)

or {tan(A+B)}{(1-tanAtanB)=tanA+tanB

When A= 36° and B=9°

then,we can write

{tan(36°+9°)}{(1-tan36°tan9°)=tan36°+tan9°

i.e. tan(45°){(1-tan36°tan9°)=tan36°+tan9°

Since tan45×=1 we have

1×{(1-tan36°tan9°)=tan36°+tan9°

or 1-tan36°tan9°=tan36°+tan9°

Hence 1=tan36°+tan9°+tan36°tan9°

or tan36°+tan9°+tan36°tan9°=1

:))