Question

if x and b are complementary angles such that cos x=square root of 3/2.Find the value of 2 sin b sin x

Answer 1

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Answer on Question #45216 – Math – Other

if x and b are complementary angles such that $\cos(x) = \frac{\sqrt{3}}{2}$. Find the value of 2 sin b sin x

Solution

If $\cos(x) = \frac{\sqrt{3}}{2}$, then $x = 30{}^\circ$ or pi/6.

Two angles are complementary when they add up to $90{}^\circ$, i.e. $x + b = 90{}^\circ$.

Knowing that b and x are complementary, we can find that $b = 90{}^\circ - x = 90{}^\circ - x = 60{}^\circ$ or pi/3.

Recall $\sin b = \sin 60{}^\circ = \frac{\sqrt{3}}{2}$, $\sin x = \sin 30{}^\circ = \frac{1}{2}$.

Then $2 \sin b \sin x = 2 \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2} = \frac{\sqrt{3}}{2}$.