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If cos3x+cosx-cos2x=0, then...

If cos3x+cosx-cos2x=0, then

A

`x=(2n+1)^(3)(pi)/(4),n inZ`

B

`x=2npi+(3pi)/(2)ninZ`

C

`x=2npi+-(4pi)/(3),ninZ`

D

`x=2npi+-(pi)/(3),ninZ`

Text Solution

Verified by Experts

The correct Answer is:
D
`cos3x+cosx-cos2x=0`
`rArr2"cos"(3x+x)/(2)"cos"(3x-x)/(2)-"cos"2x =0`
`rArr2cos2xcosx-cos2x=0`
`rArrcos2x=0or2cosx-1=0`
`rArr2x=(2n+1)(pi)/(2)or2cosx=(1)/(2)`
`rArrx=(2n+1)(pi)/(4)orcosx="cos"(pi)/(3)`
`rArrx=(2n+1)(pi)/(4)orx=2npi+-(pi)/(3),ninZ`
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