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The number of solutions of equation sin....

The number of solutions of equation `sin.(5x)/(2)-sin.(x)/(2)=2` in `[0,2pi]` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Given equation can hold only if `sin.(5x)/(2)-1` and `sin.(x)/(2)=-1`
i.e. `(5x)/(2)=2n pi +(pi)/(2)` and `(x)/(2)=2p pi -(pi)/(2)` (n `p in I`)
For some possible p and n if there exists a solution, we must have
`10 p pi-(5pi)/(2)=2n pi + (pi)/(2)`
oe `10 p - 2n = 3`
L.H.S. is even, R.H.S. is odd
Hence, not possible for any p and n.
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