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.

Sample questions

1. 1.Prove the trigonometric identity by selecting the correct simplified form of the left-hand side (LHS): $(\csc A - \sin A)(\sec A - \cos A) \sec^2 A$
   • A.$\frac{\sin A}{\cos A} = \tan A$
   • B.$\frac{\cos A}{\sin A} = \cot A$
   • C.$\frac{1}{\sin A \cos A} = \csc A \sec A$
   • D.$\sin A \cos A = \frac{1}{2} \sin 2A$
2. 2.Which of the following correctly proves the identity: $\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sec A + \tan A$?
   • A.$\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sqrt{\frac{(1 + \sin A)^2}{1 - \sin^2 A}} = \frac{1 + \sin A}{\cos A} = \sec A + \tan A$
   • B.$\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sqrt{\frac{1 - \sin A}{1 + \sin A}} = \frac{1 - \sin A}{\cos A} = \sec A - \tan A$
   • C.$\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \frac{1 + \sin A}{1 - \sin A} = \frac{1}{\cos A} = \sec A$
   • D.$\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sqrt{\frac{1 + \sin A}{1 - \sin A} \cdot \frac{\cos A}{\cos A}} = \frac{1 + \sin A}{\sin A} = \csc A + 1$
3. 3.Using tables find the value of: $\sin 9^\circ 55'$
   • A.0.1719
   • B.0.1722
   • C.0.1734
   • D.0.1707
4. 4.Prove the following trigonometric identity by selecting the correct simplified form of the left-hand side (L.H.S.): $\left(\tan A + \frac{1}{\cos A}\right)^2 + \left(\tan A - \frac{1}{\cos A}\right)^2 = ?$
   • A.$2 \left(\frac{1 + \sin^2 A}{1 - \sin^2 A}\right)$
   • B.$2 \left(\frac{1 + \sin A}{1 - \sin A}\right)$
   • C.$2(\tan^2 A + \sec^2 A)$
   • D.$\frac{2 \sin^2 A}{\cos^2 A}$
5. 5.The expression $\sqrt{\frac{\sec\theta - 1}{\sec\theta + 1}} + \sqrt{\frac{\sec\theta + 1}{\sec\theta - 1}}$ simplifies to which of the following?
   • A.$2 \sec \theta$
   • B.$2 \csc \theta$
   • C.$2 \tan \theta$
   • D.$2 \cot \theta$