Trigonometry & Inverse Trigonometry
Trigonometric Ratios & Identities
nta_pyq_2025_jan
Grade 11
Question:
If sin x + sin x = 1, x \in (0, 2 \pi ) , then (cos 12 x + tan 12 x) + 3 (cos 10 x + tan 10 x+ 2 cos 8 x + tan 8 x) + (cos 6 x + tan 6 x) is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for trigonometric identities and simplify using the given constraints.
sin x + sin x = 1 2 2 (4) \Rightarrow sin x = cos x \Rightarrow tan x = cos x \therefore Given expression 12 10 8 6 = 2 cos x + 6 [cos x + cos x] + 2 cos x 6 5 4 3 = 2 [sin x + 3 sin x + 3 sin x + sin x] 3 3 = 2 sin x [(sin x + 1) ] 3 2 = 2[sin x + sin x] = 2 ∘ ∘ ∘
Correct Answer: 4