Question

tanx +square root 3= sec x

Answer 1

isolate the x first...

tanx - secx = - sqrt 3

\[\large \frac {sinx}{cosx} - \frac {1}{cosx} = -\sqrt{3}\]
\[\large \frac {sinx-1}{cosx} = -\sqrt{3}\]

hmmmm..i may be on the right track but im stuck :/

Answer 2

\[\large \frac {sinx - (\sin ^{2}x + \cos ^{2}x)}{cosx} = -\sqrt{3}\]

Answer 3

i think im getting somewhere...

Answer 4

tanx +square root 3= sec x
tanx = secx - sqrt 3
Square both sides
(tanx)^2 = (secx - sqrt 3)^2
Given that (tanx)^2 = (secx)^2 - 1
(secx)^2 - 1 = (secx)^2 - 2sqrt 3 (secx) +3
0 = -2sqrt3 (secx) +4
secx = 2/sqrt 3
.....

Answer 5

ok I have to find all solutions in between the interval 0<x<360 degrees for this problem

Answer 6

ill leave @Callisto to this <tips hat>

Answer 7

Hold on, I need to check... sorry, just a minute

Answer 8

no problem

Answer 9

I don't know why... when i sub my solution back, i can't get the answer...:(

Answer 10

yea this is a troublesome problem for me too

Answer 11

secx = 2/sqrt 3
x = 30(rejected) or x =330
I found that another solution is 150.. but I don't know how to get it by solving the equation. Give me some more time..

Answer 12

ok

Answer 13

Alright, I got it
tanx +square root 3= sec x
Square both sides
(tanx+sqrt3)^2 = (secx)^2
Given that (tanx)^2 +1 = (secx)^2
(tanx)^2+2(sqrt3)(tanx) +(sqrt3)^2 = (tanx)^2 +1
2(sqrt3)(tanx) +3= 1
(2sqrt3) tanx = -2
tanx = -2 / (2sqrt3)
tanx = -1/sqrt3
x = 150 or x=330

Answer 14

lifesaver, thank you!!

Answer 15

Do you understand it?