Trigonometry – Verified PYQ Authority Guide
Trigonometry is a sub-subject authority hub. It is designed to expose the important topic/concept clusters represented by verified SRO PYQs and guide students from broad revision into the exact solved questions that support each area. Every factual learning cue below is drawn from the existing verified, published and approved English PYQ corpus or from its Knowledge Graph relationships; the hub does not invent unsupported technical claims.
PYQ evidence snapshot
38 verified PYQs are currently mapped to this Sub Subject hub. The represented years include 2025. Exam coverage currently includes RRB NTPC Under Graduate Level. Subject context includes Quantitative Aptitude. These values come from live mappings and can expand automatically when new verified PYQs are added.
Most useful verified PYQs to solve first
Start with the actual questions rather than memorising a generic note. The links below are ranked from the mapped corpus using repeat history and editorial quality, while the complete explanation stays on the individual question page.
- If sin 6A = cos 12A, find the value of tan 9A + cot 9A.
RRB NTPC Under Graduate Level · 2025 · Using sin θ = cos(90° − θ)
Using cos 12A = sin(90° − 12A), the standard relation gives 6A + 12A = 90°, so A = 5°. Then 9A = 45°,… - A club received an income of ₹7,643 from membership fees and ₹2,198 from selling old sports equipment during the year. At the start of the year, ₹1,105 in membership fees was outstanding,…
RRB NTPC Under Graduate Level · 2025 · Trigonometric Ratios
Use the standard Trigonometric Ratios method and simplify; the result matches ₹1,245 surplus. - A flagpole stands on top of a building. From a point 25 metres away from the base of the building, the angle of elevation to the top of the flagpole is 60°,…
RRB NTPC Under Graduate Level · 2025 · Trigonometric Ratios
Use the standard Trigonometric Ratios method and simplify; the result matches 29 m. - From the top of a building 20 m high, the angles of depression of the top and the bottom of a tower standing on the same horizontal ground are observed to be…
RRB NTPC Under Graduate Level · 2025 · Trigonometric Ratios
Use the standard Trigonometric Ratios method and simplify; the result matches 13.33 m. - If the sum of two distinct consecutive prime numbers is 36, what is the product of the two primes?
RRB NTPC Under Graduate Level · 2025 · Trigonometric Ratios
Use the standard Trigonometric Ratios method and simplify; the result matches 323. - A shirt costs ₹655. During a sale, its price is reduced by 20%. What is the new price (in ₹) of the shirt?
RRB NTPC Under Graduate Level · 2025 · Trigonometric Ratios
Use the standard Trigonometric Ratios method and simplify; the result matches 524. - Which of the expressions given below has the same value as that of cos²(θ) + sin²(θ)?
RRB NTPC Under Graduate Level · 2025 · Trigonometric Ratios
Use the standard Trigonometric Ratios method and simplify; the result matches 1 + tan²(θ) + (1- sec²(θ)). - The cost of an article is increased by 20% in the first year. In the second year the increased cost is decreased by 24%. If the final cost of the article is…
RRB NTPC Under Graduate Level · 2025 · Trigonometric Ratios
Use the standard Trigonometric Ratios method and simplify; the result matches ₹2,125.
Formula & key-relationship bank from verified solutions
cos θ = sin(90° − θ); tan 45° = 1; cot 45° = 1sin²θ + cos²θ = 1; tanθ = sinθ/cosθ; cotθ = 1/tanθ
Use these as revision triggers and open the linked PYQ before applying a formula numerically; variable definitions and assumptions belong to the exact solved question.
Core ideas repeatedly reinforced by the solved corpus
- Using cos 12A = sin(90° − 12A), the standard relation gives 6A + 12A = 90°, so A = 5°. Then 9A = 45°, and tan45° + cot45° = 1 + 1 = 2.
- Use the standard Trigonometric Ratios method and simplify; the result matches ₹1,245 surplus.
- Use the standard Trigonometric Ratios method and simplify; the result matches 29 m.
- Use the standard Trigonometric Ratios method and simplify; the result matches 13.33 m.
- Use the standard Trigonometric Ratios method and simplify; the result matches 323.
Exam tips already validated in SRO solutions
- For sin x = cos y questions, first test the complementary relation x + y = 90°; it often leads directly to a standard angle.
- Identify the Trigonometric Ratios relationship before calculation and keep units/bases consistent.
Common mistakes to avoid
- Stopping after tan45° = 1 and forgetting to add cot45° = 1.
- Using a shortcut without checking its conditions or using the wrong base/unit.
Topic and concept coverage
Mapped topic labels include Trigonometry, Trigonometric Identities. The concept trail includes Trigonometric Ratios, Using sin θ = cos(90° − θ). Use these labels as a revision map: move from the broad area to the narrow concept, solve a verified PYQ, inspect the detailed reasoning, and then attempt another question from the same cluster.
Knowledge Graph navigation
Continue with Quantitative Aptitude, Trigonometric Identities, Trigonometry, Trigonometry, Trigonometry, Trigonometry, Trigonometric Ratios, Trigonometric Ratios, Trigonometric Ratios, Trigonometric Ratios, Trigonometric Ratios. These are canonical SRO entity links based on the Knowledge Graph and shared question mappings, not keyword-stuffed tag pages.
How to revise this authority page efficiently
- Solve before reading: answer a mapped PYQ first.
- Read the exact explanation: verify the correct principle, formula, distractor logic and common mistake on that question page.
- Move one level in the graph: use the closest concept/sub-topic/topic link rather than opening unrelated content.
- Reattempt: solve another verified PYQ from this hub and check whether the same error repeats.
Quality scope: this page is automatically maintained from SRO’s verified mapped corpus. It enriches one canonical authority URL instead of generating multiple near-duplicate pages for keyword variants. Manual authority articles are never overwritten by the automated engine.