The range of variable of θ in the interval (0,π) such that the points (3,5) and (sinθ,cosθ) lie on the same side of the line x+y−1=0 , is

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(0,π2)

(0,π4)

(π4,π2)

(π4,0)

answer is A.

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Detailed Solution

L11 and L22 have same sign since L11=3+5−1>0, ∴L22=sinθ+cosθ−1>0 ⇒ sinθ+cosθ>1 ⇒sin(π4+θ)>12⇒ sin(π4+θ)>sinπ4⇒π4<θ+π4<3π4⇒ 0<θ<π2. Hence θ∈(0,π2) .

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