. Then what is θ equal to
If cosθ + √3 sinθ = √2 and 0° < θ < 180°, then what is θ equal to?
A. 15° or 105°
B. 35° or 115°
C. 25° or 110°
D. 40° or 125°
Best Answer
Correct Optio is : A
Solution :
Given : cosθ + √3 sinθ = √2
To find : Value of θ
Formula used : SinACosB+CosASinB = Sin(A+B)
We have, cosθ + √3 sinθ = √2
… (i)
⇒ θ = 15°
We know that sin(180-θ) = sinθ
Therefore from eqn. (i)
Sin(180-30-θ) = sin(45°)
⇒ 150-θ = 45
⇒ θ = 105°
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