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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-25-IDN-01
Simple Trigonometric Identities - Assignment
Chapter: Trigonometry
Topic: Simple Identities Involving sin, cos and tan
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.
$\sin^2\theta+\cos^2\theta=$
  • A.$0$
  • B.$1$
  • C.$2$
  • D.$\tan\theta$
2.
$1+\tan^2\theta=$
  • A.$\sec^2\theta$
  • B.$\operatorname{cosec}^2\theta$
  • C.$\cos^2\theta$
  • D.$1$
3.
$1+\cot^2\theta=$
  • A.$\sec^2\theta$
  • B.$\operatorname{cosec}^2\theta$
  • C.$\sin^2\theta$
  • D.$1$
4.
$\sin^2\theta=$
  • A.$1-\cos^2\theta$
  • B.$1+\cos^2\theta$
  • C.$\cos^2\theta-1$
  • D.$\cos^2\theta$
5.
$\sec^2\theta-\tan^2\theta=$
  • A.$0$
  • B.$1$
  • C.$2$
  • D.$\sin^2\theta$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $\sin\theta=\tfrac35$, find $\cos\theta$.
7.
Simplify $1-\sin^2\theta$.
8.
Simplify $\sec^2\theta-1$.
9.
If $\cos\theta=\tfrac{12}{13}$, find $\sin\theta$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Verify $\sin^2 30^\circ+\cos^2 30^\circ=1$.
11.
If $\tan\theta=\tfrac43$, find $\sec\theta$.
12.
Simplify $\dfrac{1-\cos^2\theta}{\sin\theta}$.
13.
Simplify $\sin^2\theta\cdot\operatorname{cosec}^2\theta$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Prove that $(1-\sin^2\theta)\sec^2\theta=1$.
15.
If $\sec\theta+\tan\theta=2$, find $\sec\theta-\tan\theta$ and hence $\sec\theta$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $1$
  2. (A) $\sec^2\theta$
  3. (B) $\operatorname{cosec}^2\theta$
  4. (A) $1-\cos^2\theta$
  5. (B) $1$
Section B — Short Answer (2 marks)
  1. $\tfrac45$.
  2. $\cos^2\theta$.
  3. $\tan^2\theta$.
  4. $\tfrac{5}{13}$.
Section C — Short Answer (3 marks)
  1. $\tfrac14+\tfrac34=1$.
  2. $\tfrac53$.
  3. $\sin\theta$.
  4. $1$.
Section D — Long Answer (5 marks)
  1. $\cos^2\theta\cdot\sec^2\theta=1$.
  2. $\sec\theta-\tan\theta=\tfrac12$; $\sec\theta=\tfrac54$.
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