Trigonometry
Product/sum identities at 20°
MJMT_Full_Test_11
Grade 12
Question:
The value of the expression $\dfrac{\sin 20°(4\cos 20°+1)}{\cos 20°\cdot\cos 30°}$ is
2
$\dfrac{1}{3}$
$\dfrac{1}{2}$
3
Step-by-Step Solution
Key Concept: Rewrite $\sin20°(4\cos20°+1)=2\sin40°\sin20°+2\sin60°\sin20°$... or use: $\sin20°(4\cos20°+1)=\sin20°\cdot4\cos20°+\sin20°=2\sin40°+\sin20°=2\sin(60°-20°)+\sin20°$.
Value = 2.
Correct Answer: 1