Solve for x.
tan 2x- cot 2x=0

Question

Solve for x.
tan 2x- cot 2x=0

anonymous · Answer

$$
\tan 2x - \cot 2x=0\
\tan 2x - \frac{1}{\tan 2x}=0\
\frac{\tan^22x-1}{\tan 2x}=0\
\tan^22x=1\
\tan 2x=\pm1\

$$

anonymous · Answer

tan2x=cot2x
tan2x=1/tan2x
tan^2(2x)=1
tan2x=+-1
2x=arctg(+-1)
x=1/2arctg(+-1)

anonymous · Answer

arctan1=0.785398163
arctan(-1) =-0.785398163

anonymous · Answer

Suppose that 2x= t
Then we have : tan t -cot t = 0
Tan t = ( tan t) ^ (-1)
tan^2 t = 1 

t = k$$pi$$ + $$pi$$ /4        k=0,1,2,....
 2x = t 
x = t/2

kropot72 · Answer

Starting with the identity tan 2x = (2 tanx)/(1 - tan^2 x) I obtained a quadratic in terms of x which when solved gives the following solutions for x:
x = 67.5 degrees, x = 22.5 degrees.
These solutions check out when substituted in the original equation.

anonymous · Answer

If you just convert to sin and cos u get
Sin^2(2x) = Cos^2(2x)
We (should) know that sin = cos at pi/4 or 45 degrees etc