Trigonometry & Inverse Trigonometry
Trigonometric Ratios & Identities
nta_pyq_2025_jan
Grade 11
Question:
If \sum , then a + b is equal to : 13 1 2 2 { } = a\sqrt3 + b, a, b \in Z r=1 \pi \pi \pi r\pi sin( +(r-1) ) sin( + ) 4 6 4 6
Step-by-Step Solution
Key Concept: Apply the core result for trigonometric identities and simplify using the given constraints.
\pi r\pi \pi \pi sin[( + )-( )-(r-1) ] 1 13 4 6 4 6 \pi \sum (4) r=1 \pi \pi \pi r\pi sin 6 sin( +(r-1) ) sin( + ) 4 6 4 6 13 1 \pi \pi \pi r\pi \sum (cot( + (r - 1) ) - cot( + )) \pi sin 4 6 4 6 6 r=1 = 2\sqrt 3 - 2 = \alpha \sqrt 3 + b So a + b = 82 2
Correct Answer: 4