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.Find the value of $x$, if: $\cos x = \cos 60^\circ \cos 30^\circ + \sin 60^\circ \sin 30^\circ$.
   • A.$x = 30^\circ$
   • B.$x = 60^\circ$
   • C.$x = 45^\circ$
   • D.$x = 90^\circ$
2. 2.Without using trigonometric tables, which of the following correctly proves the identity: $\sec^2 75^\circ - \cot^2 15^\circ = 1$?
   • A.$\sec^2 75^\circ - \cot^2 15^\circ = \csc^2 15^\circ - \cot^2 15^\circ = 1$ using $\sec^2 (90^\circ - \theta) = \csc^2 \theta$ and $\csc^2 \theta - \cot^2 \theta = 1$
   • B.$\sec^2 75^\circ - \cot^2 15^\circ = \tan^2 75^\circ + 1 - \cot^2 15^\circ = 1$ using $\sec^2 \theta = 1 + \tan^2 \theta$
   • C.$\sec^2 75^\circ - \cot^2 15^\circ = \cos^2 15^\circ - \tan^2 75^\circ = 1$ by converting all terms to sine and cosine
   • D.$\sec^2 75^\circ - \cot^2 15^\circ = \sec^2 15^\circ - \cot^2 75^\circ = 1$ by swapping angles directly
3. 3.Prove the trigonometric identity by selecting the correct simplified form of the left-hand side: $(1 + \cot A)^2 + (1 - \cot A)^2 =$ ?
   • A.$2 + 2\cot^2 A$, which simplifies to $2\csc^2 A$
   • B.$2 - 2\cot^2 A$, which simplifies to $2\sin^2 A$
   • C.$2\cot^2 A$, which simplifies to $2\tan^2 A$
   • D.$2 + 2\cot A$, which simplifies to $2\sec^2 A$
4. 4.Using tables, find the acute angle θ, when sin θ = 0.8229.
   • A.55° 18'
   • B.55° 23'
   • C.55° 28'
   • D.54° 23'
5. 5.If $x \cos A + y \sin A = m$ and $x \sin A - y \cos A = n$, which of the following correctly relates $x^2 + y^2$ to $m$ and $n$?
   • A.$x^2 + y^2 = m^2 + n^2$
   • B.$x^2 + y^2 = m^2 - n^2$
   • C.$x^2 + y^2 = (m + n)^2$
   • D.$x^2 + y^2 = m^2 + n^2 + 2xy \sin A \cos A$