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Chapter 3: Trigonometric Functions

NCERT Solutions for CBSE Class 10 Mathematics — 34 solved questions with detailed explanations.

34

Questions

0

Topics

Solved Questions

Q1. The value of cos²(π/4) - sin²(π/4) is:

0
1
-1
1/2

Difficulty: Easy · Topic: Trig Identities

Solution

cos²(45°) - sin²(45°) = cos(2×45°) = cos90° = 0. Alternatively: (1/√2)² - (1/√2)² = 0.

Q2. The value of sin 0° is:

0
0.707
0.5
1

Difficulty: Easy · Topic: Trig Values

Solution

sin 0° = 0.

Q3. The value of sin 30° is:

0
1.732
0.866
0.5

Difficulty: Easy · Topic: Trig Values

Solution

sin 30° = 0.5.

Q4. The value of sin 45° is:

0.866
0
0.707
1.732

Difficulty: Easy · Topic: Trig Values

Solution

sin 45° = 0.707.

Q5. The value of sin 60° is:

0.866
0.5
0.707
1

Difficulty: Easy · Topic: Trig Values

Solution

sin 60° = 0.866.

Q6. The value of sin 90° is:

0
0.866
1
1.732

Difficulty: Easy · Topic: Trig Values

Solution

sin 90° = 1.

Q7. The value of cos 0° is:

1.732
1
0.866
0

Difficulty: Easy · Topic: Trig Values

Solution

cos 0° = 1.

Q8. The value of cos 30° is:

0.707
0.5
0.866
1

Difficulty: Easy · Topic: Trig Values

Solution

cos 30° = 0.866.

Q9. The value of cos 45° is:

0.707
1.732
0.866
0

Difficulty: Easy · Topic: Trig Values

Solution

cos 45° = 0.707.

Q10. The value of cos 60° is:

0.5
0.866
1.732
0

Difficulty: Easy · Topic: Trig Values

Solution

cos 60° = 0.5.

Q11. The value of cos 90° is:

0
1
0.5
0.707

Difficulty: Easy · Topic: Trig Values

Solution

cos 90° = 0.

Q12. The value of tan 0° is:

0
0.5
0.707
1

Difficulty: Easy · Topic: Trig Values

Solution

tan 0° = 0.

Q13. The value of tan 30° is:

0.707
0.577
0.5
1

Difficulty: Easy · Topic: Trig Values

Solution

tan 30° = 0.577.

Q14. The value of tan 45° is:

1
0.866
1.732
0

Difficulty: Easy · Topic: Trig Values

Solution

tan 45° = 1.

Q15. The value of tan 60° is:

1
0.5
0.707
1.732

Difficulty: Easy · Topic: Trig Values

Solution

tan 60° = 1.732.

Q16. The value of sin(75°) is:

(√6+√2)/4
(√6-√2)/4
(√3+1)/2√2
Both A and C

Difficulty: Easy-Medium · Topic: Compound Angles

Solution

sin75° = sin(45°+30°) = sin45cos30 + cos45sin30 = (√2/2)(√3/2) + (√2/2)(1/2) = (√6+√2)/4 = (√3+1)/(2√2).

Q17. The general solution of sin x = 0 is:

x = nπ, n ∈ Z
x = (2n+1)π/2, n ∈ Z
x = 2nπ, n ∈ Z
x = nπ/2, n ∈ Z

Difficulty: Easy-Medium · Topic: General Solutions

Solution

sin x = 0 when x = 0, ±π, ±2π, ... General solution: x = nπ where n is any integer.

Q18. sin(A+B) =

sinAcosB + cosAsinB
sinAcosB - cosAsinB
cosAcosB - sinAsinB
cosAcosB + sinAsinB

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

sinAcosB + cosAsinB.

Q19. cos(A+B) =

sinAcosB - cosAsinB
cosAcosB + sinAsinB
sinAcosB + cosAsinB
cosAcosB - sinAsinB

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

cosAcosB - sinAsinB.

Q20. sin2A =

sin²A-cos²A
1-2sin²A
2sinAcosA
2cos²A-1

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

2sinAcosA.

Q21. cos2A =

2sinAcosA
cos²A - sin²A
sin²A + cos²A
2sin²A

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

cos²A - sin²A.

Q22. tan(A+B) =

tanA+tanB
tanAtanB
(tanA+tanB)/(1-tanAtanB)
(tanA-tanB)/(1+tanAtanB)

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

(tanA+tanB)/(1-tanAtanB).

Q23. The period of sinx is

4π
π/2
2π
π

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

2π.

Q24. The period of tanx is

2π
π/2
π
4π

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

π.

Q25. sin²x + cos²x =

sin2x
0
2
1

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

1.

Q26. The range of sinx is

(-∞, ∞)
[0, 2π]
[-1, 1]
[0, 1]

Difficulty: Easy-Medium · Topic: Trigonometric Functions

Solution

[-1, 1].

Q27. General solution of sinx = 0:

x = nπ/2
x = nπ
x = (2n+1)π/2
x = 2nπ

Difficulty: Easy-Medium · Topic: General Solutions

Solution

sinx = 0 ⇒ x = nπ.

Q28. General solution of cosx = 0:

x = nπ/2
x = nπ
x = (2n+1)π/2
x = 2nπ

Difficulty: Easy-Medium · Topic: General Solutions

Solution

cosx = 0 ⇒ x = (2n+1)π/2.

Q29. General solution of tanx = 0:

x = nπ/4
x = 2nπ
x = (2n+1)π/2
x = nπ

Difficulty: Easy-Medium · Topic: General Solutions

Solution

tanx = 0 ⇒ x = nπ.

Q30. General solution of sinx = 1:

x = (4n+1)π/2
x = 2nπ
x = nπ
x = (2n+1)π

Difficulty: Easy-Medium · Topic: General Solutions

Solution

sinx = 1 ⇒ x = (4n+1)π/2.

Q31. General solution of cosx = 1:

x = nπ/2
x = 2nπ
x = nπ
x = (2n+1)π/2

Difficulty: Easy-Medium · Topic: General Solutions

Solution

cosx = 1 ⇒ x = 2nπ.

Q32. General solution of sinx = -1:

x = (4n-1)π/2
x = 2nπ
x = (2n+1)π
x = nπ

Difficulty: Easy-Medium · Topic: General Solutions

Solution

sinx = -1 ⇒ x = (4n-1)π/2.

Q33. General solution of cosx = -1:

x = (2n+1)π
x = nπ/2
x = nπ
x = 2nπ

Difficulty: Easy-Medium · Topic: General Solutions

Solution

cosx = -1 ⇒ x = (2n+1)π.

Q34. General solution of sin²x = 1:

x = nπ/4
x = nπ
x = 2nπ
x = (2n+1)π/2

Difficulty: Easy-Medium · Topic: General Solutions

Solution

sin²x = 1 ⇒ x = (2n+1)π/2.

Other Chapters in Mathematics

Ch 1: Sets Ch 2: Relations & Functions Ch 4: Principle of Mathematical Induction Ch 5: Complex Numbers Ch 6: Linear Inequalities Ch 7: Permutations & Combinations Ch 8: Binomial Theorem Ch 9: Sequences & Series Ch 10: Straight Lines Ch 11: Conic Sections Ch 12: Intro to 3D Geometry Ch 13: Limits & Derivatives Ch 14: Mathematical Reasoning Ch 15: Statistics Ch 16: Probability

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