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  1. If 2cosθ – sinθ = (1 / √2) , (0° < q < 90°) the value of 2 sinθ + cosθ is
    1. 1
      2

    2. 2
    3. 3
      2
    4. 2
      3
Correct Option: C

2 cosθ – sinθ =
1
2

2sinθ + cosθ = x (Let)
On squaring and adding,
4cos²θ + sin²θ – 4 sinθ . cosθ + 4 sin²θ + cos²θ+ 4 sinθ.cosθ
=
1
2

1
+ x² = 5
2

⇒x² = 5 -
1
=
9
⇒ x =
3

222



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