If (sin θ, cos θ) and (3, 2) lie on the same side of the line x + y = 1, then θ lies between

1) (0, π/2)

2) (0, π)

3) (π/4, π/2)

4) (0, π/4)

Solution:

Let L be given line x + y – 1 = 0

L(3, 2) => 3 + 2 -1 = 4 >0

L(sin θ, cos θ) > 0

sin θ + cos θ – 1> 0

Multiply and divide by √2

√2( sin θ/√2 + cos θ/√2) > 1

√2(sin θ + 450) > 1

(sin θ + π/4) > 1/√2

=> π/4 < θ + π/4 < π/2

0< θ< π/4

Hence option (4) is the answer.

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