Introduction to Trigonometry — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Introduction to Trigonometry" — 9 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Introduction to Trigonometry" — 9 important questions with detailed answers for CB…

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Key Questions Covered:

  1. Define the six trigonometric ratios for a right triangle. State the trigonome…
  2. In a right triangle ABC with right angle at B, AB = 5 cm and AC = 13 cm. Find…
  3. Prove the identity: sin²θ + cos²θ = 1
  4. + 6 more questions in the full chapter

Solutions Summary:

Question Status
Define the six trigonometric ratios for a right triangle.… ✓ Solved
In a right triangle ABC with right angle at B, AB = 5 cm … ✓ Solved
Prove the identity: sin²θ + cos²θ = 1 ✓ Solved

Showing 3 of 9 questions

Q1: Define the six trigonometric ratios for a right triangle. State the trigonometric values for the standard angles 0°, 30°, 45°, 60°, and 90°.

Trigonometric Ratios (for a right triangle with reference angle θ): Let a right triangle have: - Opposite side (opposite to angle θ) = opposite - Adjacent side (adjacent to angle θ) = adjacent - Hypotenuse = hypotenuse The six ratios are: 1. sin θ = opposite / hypotenuse 2. cos θ = adjacent / hypo...

Q2: In a right triangle ABC with right angle at B, AB = 5 cm and AC = 13 cm. Find all six trigonometric ratios of angle A.

Given: Right triangle ABC with ∠B = 90° AB = 5 cm (side adjacent to angle A) AC = 13 cm (hypotenuse) Find: All six trigonometric ratios of angle A Step 1: Find BC (the side opposite to angle A) using Pythagorean theorem. AC² = AB² + BC² 13² = 5² + BC² 169 = 25 + BC² BC² = 144 BC = 12 cm Step 2: I...

Q3: Prove the identity: sin²θ + cos²θ = 1

Prove: sin²θ + cos²θ = 1 Proof: Consider a right triangle with: - Angle θ at one vertex - Opposite side = a - Adjacent side = b - Hypotenuse = c Step 1: Write the definitions of sin θ and cos θ. sin θ = a/c cos θ = b/c Step 2: Square both ratios. sin²θ = a²/c² cos²θ = b²/c² Step 3: Add the squar...

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