Question

solve tan x sec x - 2 tan x = 0 for all real values of x..

Answer 1

@jim_thompson5910

Answer 2

@dan815

Answer 3

sec x=2
is it the solution?

Answer 4

i wish it was that easy but its not :'( the answer has multiple solutions

Answer 5

tan(x)*sec(x) - 2*tan(x) = 0

tan(x)*[ sec(x) - 2 ] = 0

tan(x) = 0 or sec(x) - 2 = 0

tan(x) = 0 or sec(x) = 2

tan(x) = 0 or 1/cos(x) = 2

tan(x) = 0 or cos(x) = 1/2

I'll let you finish up

Answer 6

@jim_thompson5910 okay i understand.. so with that being said.. they're will be 3 different solutions, and they would be

0+kpi
2kpi + pi/3
2kpi + 5pi/3
?

Answer 7

got it

Answer 8

the kpi solution is for sin x=0 and the other two ae for sec x=2

Answer 9

it's been a while since I've done this but you have to be in radian mode and add or subtract 2pi or something

Answer 10

depends on the quadrant you're in as well .

Answer 11

okay so the answers i have to select from are sketchy so i think i picked the right one? ..

Answer 12

they made a typo

they should have 2k*pi and not just 2k

Answer 13

when you wrote

`0+kpi `
`2kpi + pi/3`
`2kpi + 5pi/3`

you have all 3 correct

Answer 14

5pi/3 is coterminal to -pi/3, so either works

Answer 15

so judging on which one is the closest... it'd be A?

Answer 16

you'll have to bring it up with your teacher so they can fix it

Answer 17

but yeah A looks closest

Answer 18

i will thanks jim you da bestttttttttttttttt

Answer 19

yw

Answer 20

when you solve it, you get sin x=0 and sec x=2 so you get the answer as given