How do you solve #Tan x + cot x -2 =0 #?

1 Answer
Burglar
Jun 18, 2016

The solution is #x=\pi/4+npi#.

Explanation:

#cot(x)=1/tan(x)# then

#tan(x)+cot(x)-2=0#

#tan(x)+1/tan(x)-2=0#

#(tan(x)^2+1-2tan(x))/tan(x)=0#

#tan(x)^2+1-2tan(x)=0#

this is a square

#tan(x)^2+1-2tan(x)=0#

#(tan(x)-1)^2=0#

doing the square root we obtain

#tan(x)-1=0#

#tan(x)=1#

#x=arctan(1)=\pi/4#.

This is called the principal solution. We know that the tangent is periodic of period #pi# then also #\pi/4+pi#, #\pi/4+2pi#, #\pi/4+3pi#, etc. are solutions.
The generic solution is then #pi/4+npi# where #n# is any positive or negative integer number.

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
21378 views around the world
You can reuse this answer
Creative Commons License