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 right-hand side: $\frac{1 - \cos A}{1 + \cos A} = (\cot A - \csc A)^{2}$. Which of the following steps correctly simplifies the right-hand side to match the left-hand side?
- A.$(\cot A - \csc A)^{2} = \frac{(1 - \cos A)^{2}}{1 - \cos^{2} A} = \frac{1 - \cos A}{1 + \cos A}$
- B.$(\cot A - \csc A)^{2} = \frac{(\cos A - 1)^{2}}{\sin^{2} A} = \frac{1 + \cos A}{1 - \cos A}$
- C.$(\cot A - \csc A)^{2} = \frac{1 - \cos^{2} A}{(1 + \cos A)^{2}} = \sin^{2} A$
- D.$(\cot A - \csc A)^{2} = \frac{(\cos A + 1)^{2}}{\sin^{2} A} = \frac{1 + \cos A}{1 - \cos A}$
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2.Which of the following correctly completes the proof that $(\sin A + \cos A)(\sec A + \csc A) = 2 + \sec A \csc A$?
- A.$(\sin A + \cos A)(\sec A + \csc A) = \tan A + \cot A + 2$
- B.$(\sin A + \cos A)(\sec A + \csc A) = \sin A \cos A + \sec A \csc A$
- C.$(\sin A + \cos A)(\sec A + \csc A) = 1 + \sec A + \csc A$
- D.$(\sin A + \cos A)(\sec A + \csc A) = 2 \tan A + 2 \cot A$
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3.(i) Using tables, find the value of: $\sin 83^\circ 12'$
- A.0.9930
- B.0.9390
- C.0.9903
- D.0.9929
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4.Prove the trigonometric identity by determining which of the following expressions correctly simplifies both sides of the equation: $\frac{\sin A}{(\cot A + \csc A)} = 2 + \frac{\sin A}{(\cot A - \csc A)}$?
- A.$1 - \cos A$ for both sides
- B.$\sin A - \cos A$ for both sides
- C.$1 + \cos A$ for the left side only
- D.$\frac{\sin A}{1 + \cos A}$ for both sides
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5.Assertion (A): If $\sin^2 A + \sin A = 1$ then $\cos^4 A + \cos^2 A = 1$ Reason (R): $1 - \sin^2 A = \cos^2 A$
- a.(A) is true, (R) is false.
- b.(A) is false, (R) is true.
- c.Both (A) and (R) are true, and (R) is the correct reason for (A).
- d.Both (A) and (R) are true, and (R) is the incorrect reason for (A).
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