Question

tan18° + tan 27° + tan 18°tan 27°​

Answer 1

tan(18∘)+tan(27∘)+tan(18∘)⋅tan(27∘) .

You should learn to switch to radians, and then simply numbers. Thus, evaluate

tan(π10)+tan(3π20)+tan(π10)⋅tan(3π20).

Now, we know that

tan(π10)+tan(3π20)1−tan(π10)⋅tan(3π20)=tan(π10+3π20)

=tan(π4)=1.I

It follows from this that

tan(π10)+tan(3π20)=1−tan(π10)tan(3π20)..

It follows that

tan(π10)+tan(3π20)+tan(π10)tan(3π20)=1.