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Equations of lines along OA , OB and AB are y = 0, x = 0, and x+y = √(3/2) respectively.
Now P and B will lie on the same side of y = 0 if cosθ > 0.
Similarly P and A will lie on the same side of x = 0 if sin θ > 0 and P and O will lie on the same side of x + y = √(3/2) if sin θ + cosθ √(3/2) .
Hence P will lie inside the Δ ABC, if sinθ > 0, cosθ > 0 and sinθ + cosθ √(3/2) .
Now sinθ + cosθ √(3/2)
⇒ sin ( θ + π /4)
i.e. 0
or, 2π/3
Since sinθ >0 and cos θ > 0, so
0
Regards
Arun (askIITians forum expert)
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