ICSE Class 10 Mathematics: Trigonometry — Important Questions with Answers 2026

Short Answer Questions (2-3 Marks)

• Q: Prove that: sin²θ + cos²θ = 1.
  Ans: In a right triangle with hypotenuse h, opposite side p, adjacent side b: sin θ = p/h, cos θ = b/h. sin²θ + cos²θ = p²/h² + b²/h² = (p² + b²)/h². By Pythagoras theorem: p² + b² = h². Therefore sin²θ + cos²θ = h²/h² = 1.
• Q: If tan θ = 3/4, find sin θ and cos θ.
  Ans: tan θ = opposite/adjacent = 3/4. Hypotenuse = √(3² + 4²) = √25 = 5. sin θ = 3/5 = 0.6. cos θ = 4/5 = 0.8. Verify: sin²θ + cos²θ = 9/25 + 16/25 = 25/25 = 1 ✓
• Q: Prove: (sin θ)/(1 - cos θ) = (1 + cos θ)/(sin θ).
  Ans: LHS = sin θ/(1 - cos θ). Multiply numerator and denominator by (1 + cos θ): = sin θ(1 + cos θ)/[(1 - cos θ)(1 + cos θ)] = sin θ(1 + cos θ)/(1 - cos²θ) = sin θ(1 + cos θ)/sin²θ = (1 + cos θ)/sin θ = RHS. Hence proved.

Long Answer / Application Questions (4-6 Marks)

• Q: From a point 30 m from the base of a tower, the angle of elevation of the top is 60°. Find the height of the tower.
  Ans: Let height = h. tan 60° = h/30. √3 = h/30. h = 30√3 = 30 × 1.732 = 51.96 m ≈ 52 m.

Exam Tips for This Chapter

• Revise all definitions and laws from Trigonometry — they are commonly asked as 1-2 mark questions
• Practice diagrams related to Trigonometry — neat labelled diagrams carry 2-3 marks
• For numericals, always show formula → substitution → answer with correct units
• Previous year analysis shows Trigonometry carries 8-12 marks in the board exam