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# Induction watch

1. Prove, by induction, that the sum from 1 to n of cos2rX is
0.5((sin(2r+1)X)/sinx +1)

I can prove it by induction, although I am not certain if my logic is correct. Could anyone try this for me? Thanks.
2. Is that : (sin(2r+1)X)/2(sinx +1)
or ((sin(2r+1)X)/2sinx) +1/2
or (sin(2r+1)X)/2sin(x +1)

?
3. pdf attached.
Attached Images
4. trigsum.pdf (25.7 KB, 103 views)
5. If you want an alternative to induction you could use complex numbers or multiply the sum by sinx and use method of differences, although since the result is given, induction works easiest here
6. The attached question (STEP 1990 Maths) is a nice example of using complex numbers to find trignometric sums.
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