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The number of solutions of equation cos2...

The number of solutions of equation `cos2x-3cos x+1=(1)/((cot2x-cotx).sin(x-pi))` in `[0,4pi]` is

A

0

B

2

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
Given equation
`2cos^(2)x-3 cos x = (sin x sin 2x)/((cos 2x.sin x-sin 2x.cos x).(-sin x))`
`therefore 2cos^(2)x-3 cos x=(2 sin^(2)x cos x)/((-sin x)(-sin x))=2cos x`
`therefore 2cos^(2)x-5 cos x = 0`
`therefore cos x =0` or `cos x = (5)/(2)`
We must have `x ne n pi, (n pi)/(2), n in Z`
Hence, no solution.
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