यदि `sin theta+2 cos theta =1` हो , तब `2 sin theta - cos theta` किसके बराबर है ?

Options

A. `0`
B. `1`
C. `2`
D. `4`

Answer

C

Explanation

` sin theta + 2 cos theta = 1`

` (sin theta + 2 cos theta ) ^(2) = 1`
` rArr sin^(2) theta + 4 cos^(2) theta+ 4 sintheta * cos theta= 1`
` rArr (1-cos^(2)theta)+4(1-sin^(2)theta)`
` + 4 sin theta * costheta=1`
` [ :' sin^(2) theta + cos^(2) theta =1 ] `
` rArr 1 - cos^(2) theta + 4-4 sin^(2) theta` ,
` + 4 sin* cos theta =1`
` rArr 4 sin^(2) theta + cos^(2) theta - 4 sin theta * cos theta = 4`
` rArr ( 2 sin theta - cos theta)^(2)= 4 = (2)^(2`
` :. 2 sin theta - cos theta =2`