Trigonometry & Inverse Trigonometry
Tan-Cot Combinations Using Complementary Angles
nta_pyq_2023_apr
Grade 11
Question:
The value of $\tan 9°-\tan 27°-\tan 63°+\tan 81°$ is _____.
Step-by-Step Solution
Key Concept: Use $\tan(90°-x)=\cot x$: $\tan81°=\cot9°$, $\tan63°=\cot27°$. Rewrite as $(\tan9°+\cot9°)-(\tan27°+\cot27°)=\frac{2}{\sin18°}-\frac{2}{\sin54°}$.
$\frac{2}{\sin18°}-\frac{2}{\sin54°}=4$.
Correct Answer: 4