Question

solve: tanx-cotx=0

Answer 1

If you add cot x to both sides, you will see that the problem says that tangent x = cotangent x.
Of course cot is the reciprocal of tangent.
There are exactly 2 numbers that are the same as their reciprocals. What are they?

Answer 2

O/A = A/O, so O^2=A^2, or O=+/-A. This is true for ? multiples of pi/2. (I left out a word where the ? is.)

Answer 3

i mostly understand what Mertsj is saying but not what @rulnick is....

Answer 4

So what number is its own reciprocal?

Answer 5

i dont know...

Answer 6

Then you must solve the equation in another way:

Answer 7

tan(x) - cot(x) = 0
(sin(x) / cos(x)) - (cos(x) / sin(x)) = 0
(sin^2(x) / sin(x)cos(x)) - (cos^2(x) / sin(x)cos(x)) = 0
(sin^2(x) - cos^2(x)) / (sin(x)cos(x)) = 0
sin^2(x) - cos^2(x) = 0
cos^2(x) - sin^2(x) = 0
cos(2x) = 0

Note that if 0 <= x <= 2pi, then 0 <= 2x <= 4pi
If cos(2x) = 0 on [0, 4pi]. we have:

2x = pi/2 or 3pi/2 or 5pi/2 or 7pi/2
x = pi/4 or 3pi/4 or 5pi/4 or 7pi/4

Answer 8

\[\frac{\sin x}{\cos x}-\frac{\cos x}{\sin x}=0\]

Answer 9

\[\frac{\sin ^2x-\cos ^2x}{\sin x \cos x}=0\]

Answer 10

tanx - cotx = 0
tan x = cot x
O/A = A/O
Cross multiply to get O^2 = A^2.
Solve to get O = plus or minus A.
So the solution is all angles x such that the opposite is +/- the adjacent.
This is true for all ______ multiples of pi/4 (or 45 degrees).
Possible fill-in-the-blanks: odd, even.

Answer 11

If a fraction is 0, it's numerator is 0.

Answer 12

So
\[\sin ^2-\cos ^2x=0\]

Answer 13

i got this. thanks @rulnick and @mertsj

Answer 14

welcome

Answer 15

Sorry. Too many cooks result in too many different approaches to the same problem and confuse the asker as we have just seen.