Trigonometry
Exact values of trig functions at 18°/36°
MJMT_Full_Test_02
Grade 12
Question:
The value of $4\cos\dfrac{\pi}{10} - 3\sec\dfrac{\pi}{10} - 2\tan\dfrac{\pi}{10}$ is equal to
$\sqrt{5}-1$
$\sqrt{5}+1$
$0$
$1$
Step-by-Step Solution
Key Concept: Use exact values: $\cos 18°=(\sqrt{10+2\sqrt{5}})/4$, and simplify. Combine everything over $\cos 18°$.
$\frac{4\cos^2 18°\cdot\cos 18°-3-2\sin 18°}{\cos 18°} = 0$.
Correct Answer: 3