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.$$3 \cos 80^{\circ} \csc 10^{\circ} + 2 \cos 59^{\circ} \csc 31^{\circ}$$ equals which of the following?
- A.3
- B.5
- C.6
- D.1
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2.Prove the trigonometric identity by selecting the correct simplification: $\tan (45^\circ - A) \tan (45^\circ + A) = 1$. Which of the following steps correctly demonstrates this identity?
- A.$\tan (45^\circ - A) \tan (45^\circ + A) = \cot (45^\circ + A) \tan (45^\circ + A) = 1$
- B.$\tan (45^\circ - A) \tan (45^\circ + A) = \tan^2 (45^\circ + A) = 1$
- C.$\tan (45^\circ - A) \tan (45^\circ + A) = \tan (90^\circ) = 1$
- D.$\tan (45^\circ - A) \tan (45^\circ + A) = \sin (45^\circ - A) \cos (45^\circ + A) = 1$
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3.$$\frac{\sin 38^{\circ}}{\csc 52^{\circ}} + \frac{\cos 52^{\circ}}{\sec 38^{\circ}}$$
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4.(iii) Using tables find the value of: $\tan 31^\circ 27'$
- A.0.6084
- B.0.6104
- C.0.6116
- D.0.6146
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5.In the given figure, AD is perpendicular to BC, $\tan B = \frac{3}{4}$ and $\tan C = \frac{5}{12}$. BC = 56 cm. Calculate the length of AD.
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