Question

Solve 1 = cot^2(x) = 8sinx, for 0(lesser-than-or-equal-to) x (lesser-than-or-equal-to) 360 degrees??

Answer 1

r u sure u have correct question? The two '=' signs?

Answer 2

sorry, 1+ cot^2.....

Answer 3

my bad. didn't press shift.

Answer 4

ahh
u could try replacing cot^2x with cosec^2x - 1 = 1/sin^2x + 1

Answer 5

but that would be 1 + coesc^2x - 1, which would be cosec^x.

Answer 6

hmm lets try this:

1 + ( 1 - sin^2x) = 8 sinx
----------
sin^2x
sin^2x + 1 - sin^2x = 8 sin^3 x
sin^3 x = 1/8
s in x = +/- 1/2

Answer 7

x = 30, 150, 210, 330 degrees

Answer 8

how did you get that??

\[1 + \cot^2x = 8sinx\]

so \[cosec^2x = 8sinx\]

now what??

Answer 9

cosec^2 x = 1 / sin^2 x

Answer 10

yes. so?

Answer 11

you replace cot^2x by cosec^2 x - 1 because cosec^2x = 1 + cot^ 2 x

Answer 12

but you can replace 1 = cot^2x by cosec^2x straight away!!

Answer 13

*1 + cot^2x

Answer 14

yea right - i didnt see the obvious! - but my method comes out with the same answer.
your way is better though!
they both come to
1 / sin^2x = 8 sinx
cross multiply:

8 sin^3 x = 1
sin^3 x = 1/8
sin x = 1/2 or -1/2

Answer 15

ohhh. cool. i didn't know how to simplify it :P

Answer 16

but it can't be -0.5, though, can it??

Answer 17

hold on - sorry - i-m prone to error today
the cube root of 1/8 is 1/2 only
so x = 30, 150 only

Answer 18

i think tahs correct now lol!

Answer 19

it's okayy, i have these weird days too :P

Answer 20

can you help me with another question??

Answer 21

ok

Answer 22

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