Does tan300−tan30=tan270?

2 Answers
F. Javier B.
Jun 25, 2018

NO. See explanation below

Explanation:

We know that 270=300−30

In goniometric circle we see that 270 does not have tangent value. But let use tangent of diference to demonstrate analitically...

We know also that tan(x−y)=tanx−tany1+tanxtany

Lets check the formula in our case

tan(270)=tan(300−30)=tan300−tan301+tan300tan30=

And identity proposed will be thrue if 1+tan300tan30=1

Lets see:
tan300=−√3
tan30=√33

tan300tan30=−√3⋅√33=−1 then denominator is 1−1=0

That means tan270 does not exist, then identity proposed is not possible

Ratnaker Mehta
Jun 25, 2018

tan300∘−tan30∘≠tan270∘.
tan270∘ is undefined.
tan300∘−tan30∘=−4√3=−43√3.

Explanation:

tan270∘ is undefined.

In fact, tan300∘−tan30∘=tan(360∘−60∘)−1√3,

=−tan60∘−1√3=−√3−1√3=−4√3=−43√3.

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