QJEEM20Ma9d74: JEE Main 2020 Mathematics - Class 11 JEEM20Ma9d74 Solution: The set of all possible values of θ in the interval (0, π ) for …

Question

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The set of all possible values of

θ

in the interval
(0,

π

) for which the points (1, 2) and (sin

θ

, cos

θ

) lie
on the same side of the line x + y = 1 is :

Accepted Answer

Let f(x, y) = x + y - 1

∵ f (1, 2) . f (\sin θ, \cos θ) > 0

\Rightarrow 2 [\sin θ + \cos θ - 1] > 0

\Rightarrow \sin θ + \cos θ > 1

\Rightarrow \sin (θ + \frac{π}{4}) > \frac{1}{\sqrt{2}}

\Rightarrow θ + \frac{π}{4} \in (\frac{π}{4}, \frac{3 π}{4})

\Rightarrow θ \in (0, \frac{π}{2})

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