01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. Evaluate: 2 sin² 30° tan 60° - 3 cos² 60° sec² 30°.
CBSE 2024 · 1 MARK
Q2. If sin θ + cos θ = √2 cos θ, then find the value of tan θ.
CBSE 2024 · 2 MARKS
Q3. In △ABC, right-angled at B, AB = 5 cm and ∠ACB = 30°. Determine the lengths of sides BC and AC.
CBSE 2024 · 3 MARKS
Q4. Prove the identity: (sin θ - 2 sin³ θ) / (2 cos³ θ - cos θ) = tan θ.
CBSE 2024 · 5 MARKS
Q5. Prove that: [tan θ / (1 - cot θ)] + [cot θ / (1 - tan θ)] = 1 + sec θ csc θ.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q6. If tan θ = 4/3, then (sin θ + cos θ) / (sin θ - cos θ) is equal to:
(A) 7 (B) 1/7 (C) -7 (D) -1/7
CBSE 2023 · 2 MARKS
Q7. If sin(A - B) = 1/2 and cos(A + B) = 1/2, where 0° < A + B ≤ 90° and A > B, find A and B.
CBSE 2023 · 3 MARKS
Q8. Prove the identity: (cos A - sin A + 1) / (cos A + sin A - 1) = csc A + cot A.
CBSE 2023 · 5 MARKS
Q9. If csc θ + cot θ = p, prove that cos θ = (p² - 1) / (p² + 1).
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q10. If sin θ = cos θ for 0° ≤ θ ≤ 90°, then find θ.
CBSE 2022 · 2 MARKS
Q11. Evaluate: (5 cos² 60° + 4 sec² 30° - tan² 45°) / (sin² 30° + cos² 30°).
CBSE 2022 · 3 MARKS
Q12. Prove that: √[(1 + sin A) / (1 - sin A)] = sec A + tan A.
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q13. If x = 2 sin² θ and y = 2 cos² θ + 1, find the value of x + y.
CBSE 2021 · 2 MARKS
Q14. If 4 tan θ = 3, evaluate: (4 sin θ - cos θ + 1) / (4 sin θ + cos θ - 1).
CBSE 2021 · 3 MARKS
Q15. Prove that: (sin A + csc A)² + (cos A + sec A)² = 7 + tan² A + cot² A.
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 1 MARK
Q16. If tan A = 3/4, find the value of (1 / sin A) + (1 / cos A).
CBSE 2020 · 3 MARKS
Q17. Prove that: [sin θ / (1 + cos θ)] + [(1 + cos θ) / sin θ] = 2 csc θ.
CBSE 2020 · 5 MARKS
Q18. If tan θ + sin θ = m and tan θ - sin θ = n, prove that m² - n² = 4√(mn).
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
For identity proofs, convert all terms into sin θ and cos θ first if you get stuck.
02
Use fundamental identity sin² θ + cos² θ = 1 to substitute expressions like 1 - sin² θ = cos² θ.
03
Memorize the exact standard table values for 30°, 45°, and 60° for quick calculation.