What angle A lies in the third quadrant and it satisfies the equation `4(sin^(2)x+cosx)=1` . What is the measure of the angle A?

Options

A. `225^(@)`
B. `240^(@)`
C. `210^(@)`
D. None of these

Answer

B

Explanation

Given equation is 4 `(sin^(2)x+cosx)=1`.
`rArr4sin^(2)x+4cosx=1`
`rArr4sin^(2)x+4cosx-1=0`
`rArr4(1-cos^(2)x)+4cosx-1=0`
`4(1-cos^(2)x)+4cosx-1=0` `rArr4-4cos^(2)x+4cosx-1=0`
`rArr-4cos^(2)x+4cosx+3=0`
`rArr4cos^(2)x-4cosx-3=0`
This is the quadratic in cos x .
`rArr4cos^(2)x-6cosx+2cosx-3=0`
`rArr(2cosx-3)(2cosx+1)=0`
`rArrcosx=(3)/(2)andcosx=-(1)/(2)`
`cosx=(3)/(2)` is not possible therefore cos x `=- (1)/(2)`
`rArrcosA=-(1)/(2)=cos210^(@)`
`rArrA=210^(@)`