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The general solution of 4 sin^4 x + cos^...

The general solution of `4 sin^4 x + cos^4x= 1` is

A

`x=2npi`

B

`x=npi+1`

C

`x=(n+2)pi`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Given ,`4sin^(4)x+cos^(4)x-1=0`
`rArr4sin^(4)x+(cos^(2)x-1)(cos^(2)x+1)=0`
`rArr4sin^(4)x-sin^(2)x(1-sin^(2)x+1)=0`
`rArr5sin^(4)-2sin^(2)x=0`
`rArrsin^(2)x(5sin^(2)x-2)=0`
`rArrsinx=0orsinx=+-sqrt((2)/(5))`
`rArrx=npiorx=npi+-sin^(-1)sqrt((2)/(5))`
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