Trigonometry and method of difference

  • Thread starter gaobo9109
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Homework Statement



Given that 1+2cosx+2cos2x+2cos3x + .................+2cosnx = sin(x+1/2)x cosec(x/2)
Prove that 1-2cosx+2cos2x-2cos3x+.................+2cos8x = cos(17/2)x sec(x/2)


Homework Equations





The Attempt at a Solution



1+2cosx+2cos2x+2cos3x + .................+2cos8x = sin(8+1/2)x cosec(x/2)

4cosx+4cos3x+4cos5x........ = ?

I don't know how to continue. Or is there another way?
 

Answers and Replies

  • #2
NascentOxygen
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1+2cosx+2cos2x+2cos3x + .................+ 2cos8x = ... eqn(1)
Substitute 2x for x, and you can say
1 + 2cos2x + 2 cos4x + 2cos6x + 2cos8x = ... eqn(2)

If you subtract double eqn(2) from eqn(1) you'll as good as have the left hand side. I don't know whether this will get you anywhere.

Also, fix up the x that should be n in your first line.
 

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