If 0° < q < 90°, the value of sin q + cos q is

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If 0° < q < 90°, the value of sin q + cos q is

1. equal to 1
2. greater than 1
3. less than 1
4. equal to 2

Correct Option: B

Z = sinθ + cosθ
⇒ Z² = sin²θ + cos²θ + 2 sinθ.cosθ
= 1 + 2 sinθ. cosθ
∵ 0 < θ < 90°
∴ sinθ < 1; cosθ < 1
∴ 2sinθ . cosθ < 1
and 2sinθcosθ > 1
⇒ Z² < 2
⇒ Z < √2