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.If $x = r \cos A \cos B$, $y = r \cos A \sin B$ and $z = r \sin A$, which of the following correctly shows that $x^2 + y^2 + z^2 = r^2$?
   • A.$x^2 + y^2 + z^2 = r^2 \cos^2 A \cos^2 B + r^2 \cos^2 A \sin^2 B + r^2 \sin^2 A = r^2$
   • B.$x^2 + y^2 + z^2 = r^2 \cos^2 A (\cos^2 B + \sin^2 B) + r^2 \sin^2 A = r^2 (\cos^2 A + \sin^2 A) = r^2$
   • C.$x^2 + y^2 + z^2 = r^2 (\cos^2 A + \sin^2 A + \cos^2 B + \sin^2 B) = 2r^2$
   • D.$x^2 + y^2 + z^2 = r^2 \cos^2 A \cos^2 B + r^2 \sin^2 A = r^2 (\cos^2 A + \sin^2 A) = r^2$
2. 2.Which of the following correctly proves the identity $\sqrt{\sec^2 A + \csc^2 A} = \tan A + \cot A$?
   • A.Square both sides, express in terms of $\sin A$ and $\cos A$, and use $\sin^2 A + \cos^2 A = 1$ to show LHS = RHS.
   • B.Square both sides, then simplify using $\sec^2 A = 1 + \tan^2 A$ and $\csc^2 A = 1 + \cot^2 A$ directly without further substitution.
   • C.Take the square root of both sides and equate $\sec A + \csc A$ to $\tan A + \cot A$ using reciprocal identities.
   • D.Multiply both sides by $\sin A \cos A$ to eliminate denominators, then simplify without squaring.
3. 3.(iii) Using the table, find the value of: $\cos 70^\circ 17'$
4. 4.Express $\cos 74^\circ + \sec 67^\circ$ in terms of trigonometric functions of angles between $0^\circ$ and $45^\circ$. Which of the following is the correct expression?
   • A.$\sin 16^\circ + \csc 23^\circ$
   • B.$\cos 16^\circ + \sec 23^\circ$
   • C.$\sin 74^\circ + \csc 67^\circ$
   • D.$\cos 23^\circ + \sec 16^\circ$
5. 5.$$\frac{\tan 19^{\circ}}{\cot 71^{\circ}}$$ is equal to which of the following?
   • A.0
   • B.1
   • C.-1
   • D.tan 52°