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Maths trig question A2

Hey guys
I need help solving this question:
cosec^2x + cotx - 1 = 0
I get two solutions which are correct but I can't get the other two
Original post by Remainresilient_
Hey guys
I need help solving this question:
cosec^2x + cotx - 1 = 0
I get two solutions which are correct but I can't get the other two


What was your method?
Original post by SeanFM
What was your method?

I subbed in 1+cot^2x for cosec^2x and I got cot^2x + cotx = 0
Original post by Remainresilient_
I subbed in 1+cot^2x for cosec^2x and I got cot^2x + cotx = 0


Perfect so far. After that?
Original post by SeanFM
Perfect so far. After that?


then I let cotx = a
so I got a^2 + a = 0
factorised that got a(a+1)=0
made a = 0 then a = -1
1/tan x = 0 (this must be wrong because I didn't get the correct two solutions from this)
1/tanx = -1. so tan x = -1 (this was correct as it led me to half the number of solutions)
There are 4 solutions and I can only get two of them correct so far
Original post by Remainresilient_
then I let cotx = a
so I got a^2 + a = 0
factorised that got a(a+1)=0
made a = 0 then a = -1
1/tan x = 0 (this must be wrong because I didn't get the correct two solutions from this)
1/tanx = -1. so tan x = -1 (this was correct as it led me to half the number of solutions)
There are 4 solutions and I can only get two of them correct so far


Were you given the range of the solutions?
Original post by SeanFM
Were you given the range of the solutions?


The range is 0 to 2pi
Original post by Remainresilient_
The range is 0 to 2pi


Okay.

If cotx = 0, as you've said 1/tanx = 0, so what does that suggest about tanx?

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