Question

Find the general solution. (Trig - Tan/Cos problem.)

Answer 1

\[\tan 2 \theta = \cot \theta\]

I figured that: \[\tan 2 \theta = \tan (\pi -2 \theta)\]

\[2 \theta = n \pi + \pi - 2 \theta\]

\[4 \theta = n \pi + \pi\]

General solution = \[\frac{ n \pi + \pi }{ 4 }\]

My book says I'm wrong? How so?

Thanks in advance!

Answer 2

tan2θ=−tan(π−2θ)

Answer 3

Ah, so I need a minus sign on the right hand side?

Answer 4

but u don't need that step..

Answer 5

?

Is my first step incorrect then?

Answer 6

first change cot θ to tanθ

Answer 7

cot θ=tan(pi/2 - θ)

Answer 8

Ah, so tan 2 theta = tan (pi/2 - 2 theta?)

Answer 9

now u'll have both sides tan..so u can equate the angles

Answer 10

No..read the statement carefully

Answer 11

right side (cotθ) can be changed to tan(pi/2-θ)..ok?

Answer 12

Okay,

Answer 13

ah! I got it, a bit slow this morning haha. I don't have to multiply cot by anything.

Thanks for your assistance!

Answer 14

u r welcome..so can u do the rest?

Answer 15

Yeah, I think so!

\[\ 2 \theta = n \pi +\frac{ \pi }{ 2} - \theta\]

\[3 \theta = n \pi + \pi/2 = \frac{ 2n \pi }{ 6 } + \frac{ \pi }{ 6 }\]

Answer 16

which is the answer my book gave me. c:

Answer 17

GOOD JOB! i think u deserve a medal!

Answer 18

Haha, thank you! I'll be sure to ping you if I need help in future. c:

Thanks again!