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 following trigonometric identity by selecting the correct simplified form of the left-hand side (L.H.S.): $\frac{\cos A}{1 - \tan A} + \frac{\sin A}{1 - \cot A} = ?$
   • A.$\cos A + \sin A$
   • B.$\frac{1}{\cos A - \sin A}$
   • C.$\cos^2 A + \sin^2 A$
   • D.$\frac{\cos A - \sin A}{\cos A + \sin A}$
2. 2.Which of the following simplifies to $\tan A$?
   • A.$\frac{\sin A - 2 \sin^3 A}{2 \cos^3 A - \cos A}$
   • B.$\frac{\sin A + 2 \sin^3 A}{2 \cos^3 A - \cos A}$
   • C.$\frac{2 \sin^3 A - \sin A}{\cos A - 2 \cos^3 A}$
   • D.$\frac{\sin A - 2 \sin^3 A}{\cos A - 2 \cos^3 A}$
3. 3.(iv) Using the table, find the value of: $\cos 85^\circ 8'$
4. 4.Eliminate $\theta$ between the equations: $x = a \sec^{3} \theta$ and $y = b \tan^{3} \theta$. Which of the following equations results from this elimination?
   • A.$\left(\frac{x}{a}\right)^{\frac{2}{3}} - \left(\frac{y}{b}\right)^{\frac{2}{3}} = 1$
   • B.$\left(\frac{x}{a}\right)^{\frac{1}{3}} + \left(\frac{y}{b}\right)^{\frac{1}{3}} = 1$
   • C.$\left(\frac{x}{a}\right)^2 - \left(\frac{y}{b}\right)^2 = 1$
   • D.$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
5. 5.Which of the following correctly proves the identity: $\tan A - \cot A = \frac{1 - 2\cos^2 A}{\sin A \cos A}$?
   • A.$\tan A - \cot A = \frac{\sin A}{\cos A} - \frac{\cos A}{\sin A} = \frac{\sin^2 A - \cos^2 A}{\sin A \cos A} = \frac{1 - 2\cos^2 A}{\sin A \cos A}$
   • B.$\tan A - \cot A = \frac{\sin A - \cos A}{\cos A \sin A} = \frac{1 - 2\cos^2 A}{\sin A \cos A}$
   • C.$\tan A - \cot A = \frac{\sin^2 A + \cos^2 A}{\sin A \cos A} = \frac{1 - 2\cos^2 A}{\sin A \cos A}$
   • D.$\tan A - \cot A = \frac{\sin A}{\cos A} - \frac{\cos A}{\sin A} = \frac{2\cos^2 A - 1}{\sin A \cos A}$