First slide

Compound angles

Question

If $0 < θ < \frac{π}{2}$ and $2 \sin θ = \sqrt{3} \cos 10^{0} + \sin 10^{0}$ then $θ =$

Moderate

A

$70^{0}$
B

$50^{0}$
C

$60^{0}$
D

$40^{0}$

Solution

$\sin θ = \frac{\sqrt{3}}{2} \cos 10^{0} + \frac{1}{2} \sin 10^{0} = \sin (60^{0} + 10^{0}) = \sin 70^{0}$

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