Question

Find the angles between o degrees and 360 degrees which satisfy the following equation :

tan 5x=tan 2x

Answer 1

180 degees

Answer 2

the answer behind says : 60,120,180,240 and 300 degrees.

Answer 3

theres multiple answers

Answer 4

its should = 0

Answer 5

dont have to = 0 but for 180 or 360 both side = 0

Answer 6

Recall that the following property of the tangent function as a consequence of its period:\[\tan(x+90)=\tan(x)\]Thus, we can say\[\tan(5x+180n)=\tan(2x)\text{, where } n\in\mathbb Z\]Take the arctangent of both sides (remember that the arctangent function is domain-restricted for -90<x<90):\[5x+180n=2x\text{, where } n\in\mathbb Z\]Solve for x, taking note that since n is an arbitrary integer, and since integers can be either negative or positive, it is reasonable to say that -n=n.\[x=60n\text{, where } n\in\mathbb Z\]Applying the restriction, we get the set of solution values:\[x=\left\{0,60,120,180,240,300,360\right\}\]

Answer 7

My apologies, the first equation above should be \[\tan(x+180)=\tan(x)\]