Does #tan300-tan30=tan270#?

2 Answers
Jun 25, 2018

Answer:

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-tany)/(1+tanxtany)#

Lets check the formula in our case

#tan(270)=tan(300-30)=(tan300-tan30)/(1+tan300tan30)=#

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

Lets see:
#tan300=-sqrt3#
#tan30=sqrt3/3#

#tan300tan30=-sqrt3·sqrt3/3=-1# then denominator is #1-1=0#

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

Jun 25, 2018

Answer:

#tan300^@-tan30^@!=tan270^@#.
#tan270^@# is undefined.
#tan300^@-tan30^@=-4/sqrt3=-4/3sqrt3#.

Explanation:

#tan270^@# is undefined.

In fact, #tan300^@-tan30^@=tan(360^@-60^@)-1/sqrt3#,

#=-tan60^@-1/sqrt3=-sqrt3-1/sqrt3=-4/sqrt3=-4/3sqrt3#.