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The values of x for sinx+sqrt(3)cosx=sqr...

The values of x for `sinx+sqrt(3)cosx=sqrt(2)` are

A

`2npi-(5pi)/(12)`

B

`2npi-(6pi)/(12)`

C

`2npi-(pi)/(12)`

D

`2npi+(pi)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `sqrt(3)cosx+sinx=sqrt(2)`
`rArr(sqrt(3))/(2)"cos"x+(1)/(2) "sin "x=(sqrt(2))/(2)=(1)/(sqrt(2))`
`rArr"cos"(pi)/(6)"cos" x+"sin"(pi)/(6)"sin"x=cos((pi)/(4))` `rArrcos(x-(pi)/(6))="cos"((pi)/(4))`
`rArrx-(pi)/(6)=2npi+-(pi)/(4)`
`rArrx=2npi+-(pi)/(4)+(pi)/(6)`
`rArrx=2npi+(5pi)/(12)andx=2npi-(pi)/(12)`
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