ICSE Class 10 Trigonometric Identities — Mock Test (2027)
Free online mock test for Trigonometric Identities (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Trigonometric Identities chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.Prove the trigonometric identity by selecting the correct simplification of the left-hand side: $\frac{\cosec \theta + 1}{\cosec \theta - 1} = \frac{1 + \sin \theta}{1 - \sin \theta}$
- A.$\frac{\frac{1}{\sin \theta} + 1}{\frac{1}{\sin \theta} - 1} = \frac{1 + \sin \theta}{1 - \sin \theta}$
- B.$\frac{1 + \sin \theta}{1 - \sin \theta} = \frac{\cosec \theta - 1}{\cosec \theta + 1}$
- C.$\frac{\cosec \theta + 1}{\cosec \theta - 1} = \frac{\sin \theta + 1}{\sin \theta - 1}$
- D.$\frac{1 + \sin \theta}{1 - \sin \theta} = \frac{\sec \theta + 1}{\sec \theta - 1}$
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2.Which of the following methods correctly proves the identity: $\frac{\sec A - \tan A}{\csc A + \cot A} = \frac{\csc A - \cot A}{\sec A + \tan A}$?
- A.Apply $\sec^2 A - \tan^2 A = 1$ and $\csc^2 A - \cot^2 A = 1$ to factorize and equate both sides.
- B.Multiply numerator and denominator of both sides by $\sec A + \tan A$ and $\csc A - \cot A$ respectively.
- C.Convert all trigonometric functions to sine and cosine, then cross-multiply to verify equality.
- D.Use the identity $\sec A \csc A = \tan A + \cot A$ to simplify and equate both sides.
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3.Which of the following expressions is equal to $\cot^2 A - \cot^2 B$ and completes the given identity? $\cot^2 A - \cot^2 B = \frac{\cos^2 A - \cos^2 B}{\sin^2 A \sin^2 B} = \ldots$
- A.$\frac{\sin^2 A - \sin^2 B}{\cos^2 A \cos^2 B}$
- B.$\csc^2 A - \csc^2 B$
- C.$\frac{\cos^2 A - \cos^2 B}{\cos^2 A \cos^2 B}$
- D.$\sec^2 A - \sec^2 B$
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4.(i) Using tables, find the acute angle θ, when sin θ = 0.36.
- A.21° 6'
- B.15° 42'
- C.36°
- D.21.6°
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5.Prove the following trigonometric identity by selecting the correct simplified form of the left-hand side (LHS) after applying sum-to-product identities and the given condition $A + B = 90^\circ$: $\frac{\sin A + \sin B}{\sin A - \sin B} + \frac{\cos B - \cos A}{\cos B + \cos A} = ?$
- A.$\frac{2}{\sin (A - B)}$
- B.$\frac{2}{\cos (A - B)}$
- C.$\tan A + \tan B$
- D.$\frac{2 \sin (A + B)}{\sin^2 A - \sin^2 B}$
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