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# Trig help needed! Watch

1. Find, for 0<x< pi, all the solutions of the equation

cosecx - 8 cosx = 0

2. Here it's easier to think of cosecx as 1/sinx. Doing this, add 8cosx to both sides, times both sides by sinx then use a trig identity involving sin2x.
3. Yeah I got that far, so using 1/sinx:

1/sinx - 8 cosx = 0
1/sinx = 8 cosx

if you times both sides by sinx

1 = 8 cosxsinx

So how do you then use the identity for sin2x?
4. (Original post by gluestick)
Yeah I got that far, so using 1/sinx:

1/sinx - 8 cosx = 0
1/sinx = 8 cosx

if you times both sides by sinx

1 = 8 cosxsinx

So how do you then use the identity for sin2x?
We know sin2x=2sinxcosx and 8cosxsinx=4*2sinxcosx so 8cosxsinx=4sin2x.

Therefore, sin2x = 1/4

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Updated: December 8, 2010
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