SOLUTION: solve tanx- 1=0 for all values of x.

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Question 816119: solve tanx- 1=0 for all values of x.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
tan(x) - 1 = 0
Add 1:
tab(x) = 1
We should recognize that 1 is a special angle value for tan. It tells us that the reference angle is pi%2F4. Since the 1 is positive and since tan is positive in the 1st and 3rd quadrants, we should get the following general solution equations:
x+=+pi%2F4%2B2pi%2An (for the 1st quadrant)
x+=+pi%2Bpi%2F4%2B2pi%2An (for the 3rd quadrant)
The second equation simplifies:
x+=+5pi%2F4%2B2pi%2An

Since the problem asks for all values of x, the general solution is the answer:
x+=+pi%2F4%2B2pi%2An
x+=+5pi%2F4%2B2pi%2An

P.S. Since the period of tan (and cot) is pi. The general solution can be expressed in a single equation:
x+=+pi%2F4%2Bpi%2An
(Note that the "2" is gone.)