Question

Trigonometry Help, just a bit confused with one part
@ganeshie8

Answer 1

Ill post my work on it so far and you can see if ive done it right but im as far as i can go without getting stuck

Answer 2

my first step^

Answer 3

hold up

Answer 4

kk

Answer 5

\[\large \sec^2x - 2\tan^2x = -2\]

Answer 6

\[\large 1+ \tan^2 x - 2\tan^2x = -2\]

Answer 7

\[\large 1-\tan^2x = -2\]

Answer 8

\[\large \tan^2x = 3\]

Answer 9

\[\large \tan x = \pm \sqrt{3}\]

Answer 10

this way, it looks bit simple right ?

Answer 11

oh wow yes i see exactly what you did. cant believe i didnt see that

Answer 12

if i woulda done it the long way, i would still come out wiht the same answer though right?

Answer 13

yes ! all roads lead to the same destination

Answer 14

awesome! wow that problem was so so so much easier your way ahha

Answer 15

all roads lea to Roma hehe

Answer 16

lol

Answer 17

alright so i get pi/3, 5pi/3, 5pi/3 do i need to put 5pi/3 twice or just put it once?

Answer 18

lol okay finding solutions for \(\large \tan x = \pm \sqrt{3}\) can be tricky as the period is NOT same as sin or cos... keepin mind the period of tan is pi, NOT 2pi.

Answer 19

oh goodness so i have to do it a diff way? i cant just do inverse tan of sqrt 3?

Answer 20

yes, instead of adding 2pi, you need to add pi

Answer 21

ooh i use the tan x = sinx/cosx?

Answer 22

so it would be (sin sqrt3)/(cos sqrt3)?

Answer 23

\(\large \tan x = \sqrt{3}\) :

since \(\pi/3\) is one solution,
pi/3 + pi = \(4\pi/3\) is also a solution

Answer 24

ok so i was totally wrong

Answer 25

how do we know Pi/3 is a solution exactly?

Answer 26

short answer :

we knw \(\pi/3\) is a solution cuz
\(\large \tan(\pi/3) = \sqrt{3}\)

Answer 27

hmm i think i udnerstand that, so are there more solutions or are there just 2?

Answer 28

oh wow that link is awesome lol

Answer 29

\(\large \tan x = -\sqrt{3}\) gives you two more solutions

Answer 30

scroll down to see the "Solutions"

Answer 31

yeah im seeing it now, thanks