Trigonometry & Inverse Trigonometry
Product of Cosines — Exact Evaluation
nta_pyq_2026_jan
Grade 11
Question:
The value of $\dfrac{\sqrt{3}\,\text{cosec}\,20°-\sec20°}{\cos20°\cos40°\cos60°\cos80°}$ is equal to
Step-by-Step Solution
Key Concept: Numerator: $\sqrt{3}\text{cosec}20°-\sec20°=\dfrac{\sqrt{3}\cos20°-\sin20°}{\sin20°\cos20°}=\dfrac{2\cos50°}{\frac{1}{2}\sin40°}=\dfrac{4\cos50°}{\sin40°}=4$.
64.
Correct Answer: 3