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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-09-CMP-01
Complementary Angles — Assignment
Chapter: Trigonometry
Topic: Problems Involving Complementary Angles
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$\sin(90^\circ-\theta)=$
  • A.$\sin\theta$
  • B.$\cos\theta$
  • C.$\tan\theta$
  • D.$\cot\theta$
2.
$\cos(90^\circ-\theta)=$
  • A.$\cos\theta$
  • B.$\sin\theta$
  • C.$\tan\theta$
  • D.$\sec\theta$
3.
$\tan(90^\circ-\theta)=$
  • A.$\tan\theta$
  • B.$\cot\theta$
  • C.$\sec\theta$
  • D.$\csc\theta$
4.
$\sec(90^\circ-\theta)=$
  • A.$\sec\theta$
  • B.$\csc\theta$
  • C.$\cos\theta$
  • D.$\tan\theta$
5.
$\sin(90^\circ-30^\circ)=$
  • A.$\tfrac12$
  • B.$\tfrac{\sqrt3}{2}$
  • C.$1$
  • D.$0$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Evaluate $\dfrac{\sin 35^\circ}{\cos 55^\circ}$.
7.
Evaluate $\tan 20^\circ\cdot\tan 70^\circ$.
8.
Express $\cos 40^\circ$ in terms of a sine.
9.
Evaluate $\cos 48^\circ-\sin 42^\circ$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Evaluate $\dfrac{\sin 18^\circ}{\cos 72^\circ}+\dfrac{\cos 15^\circ}{\sin 75^\circ}$.
11.
Evaluate $\tan 10^\circ\tan 15^\circ\tan 75^\circ\tan 80^\circ$.
12.
Show that $\sin(50^\circ+\theta)-\cos(40^\circ-\theta)=0$.
13.
Evaluate $\sec 70^\circ\sin 20^\circ+\cos 20^\circ\csc 70^\circ$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Without using tables, evaluate $\dfrac{\cos^2 20^\circ+\cos^2 70^\circ}{\sin^2 59^\circ+\sin^2 31^\circ}$.
15.
If $\sec 5A=\csc(A+36^\circ)$ where $5A$ is acute, find $A$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\cos\theta$
  2. (B) $\sin\theta$
  3. (B) $\cot\theta$
  4. (B) $\csc\theta$
  5. (B) $\tfrac{\sqrt3}{2}$
Section B — Short Answer (2 marks)
  1. $1$.
  2. $1$.
  3. $\sin 50^\circ$.
  4. $0$.
Section C — Short Answer (3 marks)
  1. $2$.
  2. $1$.
  3. $0$.
  4. $2$.
Section D — Long Answer (5 marks)
  1. $1$.
  2. $A=9^\circ$.
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