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If the points (-2,0) ,(-1,1/sqrt3) and (...

If the points (-2,0) ,(-1,`1/sqrt3`) and (` cos theta, sin theta`) are collinear then the number of value of `theta` is :

Text Solution

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As these three points are collinear, the area formed by a triangle formed by joining these three points will be `0`.
`:. |[-2,0,1],[-1,1/sqrt3,1],[costheta,sintheta,1]| = 0`
`=>-2(1/sqrt3-sintheta)+1(-sintheta-costheta/sqrt3) = 0`
`=>2sintheta-sintheta-costheta/sqrt3 = 2/sqrt3`
`=>sintheta-costheta/sqrt3 = 2/sqrt3`
`=>sqrt3/2sintheta-1/2costheta = 1`
`=>cos(pi/6)sintheta-sin(pi/6)costheta = sin(pi/2)`
`=>sin(theta - pi/6) = sin(pi/2)`
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