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If the equation cos3xcos^(3)x+sin3xsin^(...

If the equation `cos3xcos^(3)x+sin3xsin^(3)x=0`, then x is equal to

A

`(2n+1)(pi)/(4)`

B

`(2n-1)(pi)/(4)`

C

`(npi)/(4)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`becausesin3x=3sinx-4sin^(3)x`
`thereforesin^(3)x=(1)/(4)(3sinx-sin3x)`
`thereforesin^(3)x=(1)/(4)(3sinx-sin3x)`
and `cosx=4cos^(3)x-3cosx`
`rArrcos^(3)x=(1)/(4)(cos3x+3cosx)`
`thereforecos3xcos^(3)x+sin3xsin^(3)x`
`=(1)/(4)[cos^(2)3x+3cosxcos3x+3sinxsin3x-sin^(2)3x]`
`=(1)/(4)[3cos2x+cos6x]=cos^(3)2x`
`rArrcos2x=0`
`rArr2x=(2n+1)(pi)/(2)`
`rArrx=(2n+1)(pi)/(4)`
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