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.Which of the following correctly proves the identity: $\frac{1}{1 - \sin A} + \frac{1}{1 + \sin A} = 2 \sec^2 A$?
- A.$\frac{1}{1 - \sin A} + \frac{1}{1 + \sin A} = \frac{2}{1 - \sin^2 A} = \frac{2}{\cos^2 A} = 2 \sec^2 A$
- B.$\frac{1}{1 - \sin A} + \frac{1}{1 + \sin A} = \frac{2}{1 + \sin^2 A} = \frac{2}{\cos^2 A} = 2 \sec^2 A$
- C.$\frac{1}{1 - \sin A} + \frac{1}{1 + \sin A} = \frac{2\sin A}{1 - \sin^2 A} = 2 \sec A \tan A$
- D.$\frac{1}{1 - \sin A} + \frac{1}{1 + \sin A} = \frac{2}{1 - \sin A} = 2 \csc^2 A$
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2.Using tables, find the acute angle θ, when sin θ = 0.8229.
- A.55° 18'
- B.55° 23'
- C.55° 28'
- D.54° 23'
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3.(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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4.Which of the following correctly proves the identity $\sqrt{\frac{1 + \cos A}{1 - \cos A}} = (\csc A + \cot A)$?
- A.$\sqrt{\frac{1 + \cos A}{1 - \cos A}} = \sqrt{\frac{(1 + \cos A)^2}{1 - \cos^2 A}} = \frac{1 + \cos A}{\sin A} = \csc A + \cot A$
- B.$\sqrt{\frac{1 + \cos A}{1 - \cos A}} = \sqrt{\frac{1 - \cos^2 A}{(1 - \cos A)^2}} = \frac{\sin A}{1 - \cos A} = \sec A + \tan A$
- C.$\sqrt{\frac{1 + \cos A}{1 - \cos A}} = \frac{1 + \cos A}{\sqrt{1 - \cos^2 A}} = \frac{1 + \cos A}{\sin A} = \csc A - \cot A$
- D.$\sqrt{\frac{1 + \cos A}{1 - \cos A}} = \sqrt{\frac{1 + \cos A}{1 - \cos A} \cdot \frac{1 - \cos A}{1 - \cos A}} = \frac{1 - \cos A}{\sin A} = \csc A - \cot A$
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5.Prove the following trigonometric identity by selecting the correct simplified form of the left-hand side (L.H.S.): $\frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} = ?$
- A.$\sec A \csc A + 1$
- B.$\frac{1 + \sin A \cos A}{\sin A + \cos A}$
- C.$\frac{\sin A + \cos A}{\sin A \cos A}$
- D.$\sec A + \csc A$
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