Trigonometry
Introduction to Trigonometry
Trigonometric ratios, standard angles, identities.
7 marks
Board exam weightage (out of 80)
44
Worked examples on this page
Trigonometry
Unit
About this chapter
Introduction to Trigonometry covers the six trigonometric ratios of acute angles in a right triangle, values at standard angles (0°, 30°, 45°, 60°, 90°), the trigonometric identities (sin²θ + cos²θ = 1 and its companions for sec, cot, and tan), and using identities to simplify expressions or prove other relations. The chapter is worth around 12 marks across the trigonometry unit. Board questions mix one-mark direct-value MCQs with three- to five-mark prove-the-identity or evaluate-the-expression problems.
Key topics covered
- •Trigonometric ratios in a right triangle
- •Values at standard angles (0°, 30°, 45°, 60°, 90°)
- •Trigonometric identities (sin²θ + cos²θ = 1 and companions)
- •Simplifying trigonometric expressions
- •Proving trigonometric identities
Common question types in board exam
The patterns that recur most often across recent CBSE papers in this chapter.
trigonometric identity· 69 questionstrigonometric ratios· 66 questionssimplify· 58 questionsevaluate· 53 questionstrigonometric identities· 52 questionstrigonometric ratio· 34 questions
Question difficulty mix
Count of questions seen across all CBSE papers we've indexed, by mark value.
137×1-mark
60×2-mark
63×3-mark
Worked solutions (44)
Grouped by year and tier2026 standard
- If , then find the value of .Set 1 Part 1 · Q24 · 2 marks
- If , , then prove that:Set 1 Part 1 · Q28 · 3 marks
- If , then find the value of .Set 1 Part 3 · Q22 · 2 marks
- Prove that : Set 4 Part 2 · Q30 · 3 marks
- (a) Prove that:…Set 4 Part 3 · Q21 · 2 marks
- (a) Evaluate: Set 5 Part 1 · Q24 · 2 marks
- Prove that:…Set 5 Part 1 · Q28 · 3 marks
2026 basic
- Prove that geometrically.Set 1 Part 2 · Q22 · 2 marks
- Prove that geometrically.Set 1 Part 3 · Q25 · 2 marks
- T is a point on the line PS produced of a parallelogram PQRS and QT intersects RS at V. Prove that…Set 2 Part 1 · Q30 · 3 marks
- Prove that: Set 3 Part 1 · Q29 · 3 marks
- Prove the following trigonometric identity:Set 3 Part 2 · Q27 · 3 marks
- If and , then verify that…Set 4 Part 3 · Q21 · 2 marks
- (a) Prove that Set 4 Part 3 · Q26 · 3 marks
- Prove that: .Set 5 Part 2 · Q30 · 3 marks
- (a) If and , then find the value of .Set 5 Part 3 · Q24 · 2 marks
2025 standard
- (a) If , then find the value of .Set 1 Part 1 · Q21 · 2 marks
- (a) Prove that:…Set 1 Part 1 · Q27 · 3 marks
- Solve for x and y:Set 1 Part 2 · Q24 · 2 marks
- (a) If , then find the value of .Set 1 Part 3 · Q22 · 2 marks
- (a) Prove that:…Set 1 Part 3 · Q28 · 3 marks
- If ; where A is an acute angle, then find the value of .Set 2 Part 1 · Q23 · 2 marks
- Prove that:…Set 2 Part 1 · Q27 · 3 marks
- If ; where A is an acute angle, then find the value of .Set 2 Part 2 · Q25 · 2 marks
- Prove that: Set 2 Part 2 · Q26 · 3 marks
- In the given figure, circumscribes a circle. If cm, cm and cm, find…Set 2 Part 3 · Q24 · 2 marks
- Find the value of k for which the following pair of linear equations will have infinitely many solutions:…Set 3 Part 3 · Q30 · 3 marks
- Prove that the tangents drawn at the ends of a diameter of a circle are parallel.Set 4 Part 1 · Q24 · 2 marks
- A, B and C are vertices of . Points P and Q lie on s…Set 4 Part 1 · Q29 · 3 marks
- If and , prove that Set 4 Part 2 · Q31 · 3 marks
- Find the coordinates of the points of trisection of line segment joining the points and .Set 5 Part 1 · Q23 · 2 marks
- From each end of a solid cylinder of height cm and base radius cm, a cone of base radius cm and…Set 5 Part 1 · Q30 · 3 marks
- If , then express and in terms of y.Set 5 Part 2 · Q25 · 2 marks
- (a) If and , prove that…Set 6 Part 2 · Q24 · 2 marks
- A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find …Set 6 Part 3 · Q21 · 2 marks
2025 basic
- Prove that:Set 1 Part 1 · Q30 · 3 marks
- Prove the following trigonometric identity:Set 1 Part 2 · Q28 · 3 marks
- Prove that geometrically.Set 1 Part 3 · Q25 · 2 marks
- Evaluate:Set 2 Part 1 · Q24 · 2 marks
- Prove the following trigonometric identity:Set 2 Part 1 · Q30 · 3 marks
- Evaluate:Set 2 Part 3 · Q25 · 2 marks
- Prove the following trigonometric identity:Set 2 Part 3 · Q26 · 3 marks
- Prove that:Set 3 Part 1 · Q29 · 3 marks
- Prove that…Set 6 Part 2 · Q27 · 3 marks