Trigonometry
Product of sines; identity reduction
MJMT_Full_Test_02
Grade 12
Question:
Value of $\sin32°\cdot\sin88°\cdot\sin152°$ equals
$\sin6°$
$\dfrac{\sin6°}{4}$
$\cos6°$
$\dfrac{\cos6°}{4}$
Step-by-Step Solution
Key Concept: $\sin152°=\sin28°$. Use product $\sin\alpha\sin(60°-\alpha)\sin(60°+\alpha)=\frac14\sin3\alpha$? Not quite same form. Use $\sin32°\sin88°\sin28°$: write as $\sin32°\sin28°\sin88°$. $\sin32°\sin28°=\frac12[\cos4°-\cos60°]=\frac12[\cos4°-1/2]$. Then $\times\sin88°=\cos2°$... Simplify to $\cos6°/4$.
$\dfrac{\cos6°}{4}$.
Correct Answer: 4