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Class 10 Maths Exercise 8.2 | Trigonometry NCERT Solutions | Full Explanation in Hindi
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In this video, we’ll cover Exercise 8.2 from Chapter 8: Trigonometry (NCERT) with detailed step-by-step solutions in simple Hindi. Perfect for CBSE 2025 Board Exam preparation!

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Exercise 8.2 – Class 10 Maths NCERT (Chapter 8: Introduction to Trigonometry)
Here are the NCERT solutions for Exercise 8.2 step-by-step:


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🔷 Q1. Evaluate the following:

(i) sin 60° cos 30° + sin 30° cos 60°
We use:

sin 60° = √3/2

cos 30° = √3/2

sin 30° = 1/2

cos 60° = 1/2


Solution:
= (√3/2 × √3/2) + (1/2 × 1/2)
= (3/4) + (1/4) = 1


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(ii) 2tan 45° / (1 + tan² 45°)
We know: tan 45° = 1

Solution:
= 2 × 1 / (1 + 1²)
= 2 / (1 + 1) = 1


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(iii) sin²30° + cos²30°
We know:

sin 30° = 1/2

cos 30° = √3/2


Solution:
= (1/2)² + (√3/2)²
= 1/4 + 3/4 = 1


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(iv) 2sin²60° + cos²45° - tan²30°
Values:

sin 60° = √3/2

cos 45° = 1/√2

tan 30° = 1/√3


Solution:
= 2(3/4) + (1/√2)² - (1/√3)²
= 3/2 + 1/2 - 1/3
= (3/2 + 1/2) - 1/3 = 2 - 1/3 = 5/3


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🔷 Q2. Evaluate:

(i) (sin 30° + cos 30°)² + (sin 30° - cos 30°)²
We use identity:
(a + b)² + (a - b)² = 2(a² + b²)

Let:

sin 30° = 1/2

cos 30° = √3/2


Solution:
= 2[(1/2)² + (√3/2)²] = 2[1/4 + 3/4] = 2 × 1 = 2


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(ii) (2tan30°) / (1 + tan²30°)
tan 30° = 1/√3

Solution:
= 2 × (1/√3) / (1 + 1/3)
= (2/√3) / (4/3) = (2/√3) × (3/4) = (6/4√3) = (3/2√3)

Rationalizing:
= (3√3) / (2×3) = √3/2


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(iii) tanA × cotB + sinA × secB - cosA × cosecB
Given: A = 30°, B = 60°
Use:

tan 30° = 1/√3, cot 60° = 1/√3

sin 30° = 1/2, sec 60° = 2

cos 30° = √3/2, cosec 60° = 2/√3


Solution:
= (1/√3)(1/√3) + (1/2)(2) - (√3/2)(2/√3)
= (1/3) + 1 - 1 = 1/3