f 2tanx/1-tan^2 x = 1 then x can equal:? there can be more than 1 answer x= 7pi/8 + npi x= 5pi/8 + npi x= 3pi/8 + npi x= pi/8 + npi

Question

anonymous · Answer

*if

jhannybean · Answer

think about where tan (x) cannot be defined.

anonymous · Answer

do you mean where it would not be positive on the unit circle?

anonymous · Answer

would it be: pi/8 and 7pi/8 then?

anonymous · Answer

wait, not 7pi but 5pi/8?

anonymous · Answer

is that right?

jhannybean · Answer

OR we can solve it this way - $$\large \frac{2\tan(x)}{1-\tan^2(x)}= 1$$ the function will not exist when the denominator = 0 , so let's solve for the denominator. $$\large 1-\tan^2(x)= (a-b)^2 = (1-\tan(x))(1+\tan(x))$$

jhannybean · Answer

$$\large (1-\tan(x))(1+\tan(x)) = 0$$ once you find your values for tan(x) you will see that these points create vertical asymptotes for your graph.

anonymous · Answer

Ok. That makes more sense! Thank you!

jhannybean · Answer

np :)