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If the equation (4cos^(2)x -2 sinx -3) s...

If the equation `(4cos^(2)x -2 sinx -3`) sin x, then x is equal to `(n in Z)`

A

`n pi+((3pi)/(10))`

B

`n pi+(-1)^(n+1)((3pi)/(10))`

C

`n pi+((3pi)/(10))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have `[4 cos^(2) x-2 sin x-3] sin x =0`
`rArr sin x = 0` or `4(1-sin^(2)x)-2 sin x -3 =0`
`rArr sin x =0` or `4sin^(2) x+2 sin x -1=0`
`rArr sin x=0` or `sin. X = (sqrt(5)-1)/(4),-(1+sqrt(5))/(4)`
`rArr x = n pi` or `x = n pi + (-1)^(n)(pi)/(10)`
or `x = n pi + (-1)^(n+1)((3pi)/(10)), n in Z`
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