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How do you solve #tan^2x-3=0# and find all solutions in the interval #0<=x<360#?

Answer 1

Oliver Atkinson

#x=60^circ,120^circ,240^circ,300^circ.#

Here,

#tan^2x-3=0#

#=>tan^2x=3=(sqrt3)^2#

#=>tanx=+-sqrt3,where,x in [0,360)#

We have two option:

#(1)tanx=sqrt3=>x=60^circ,240^circ#

#(2)tanx=-sqrt3=>x=120^circ,300^circ#

From, #(1)and(2)#

#x=60^circ,120^circ,240^circ,300^circ.#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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How do you solve #tan^2x-3=0# and find all solutions in the interval #0&lt;=x&lt;360#?

How do you solve #tan^2x-3=0# and find all solutions in the interval #0<=x<360#?