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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-03-TRI-01
Trigonometric Functions & Identities — Assignment
Chapter: Trigonometric Functions
Topic: Trigonometric Functions and Identities
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.$\tan^2\theta$
2.
$\cos 60^\circ=$
  • A.$\tfrac{\sqrt3}{2}$
  • B.$\tfrac12$
  • C.$1$
  • D.$0$
3.
$1+\cot^2\theta=$
  • A.$\sec^2\theta$
  • B.$\csc^2\theta$
  • C.$\tan^2\theta$
  • D.$1$
4.
$\sin 90^\circ=$
  • A.$0$
  • B.$1$
  • C.$\tfrac12$
  • D.$-1$
5.
$\tan 45^\circ=$
  • A.$0$
  • B.$1$
  • C.$\sqrt3$
  • D.$\tfrac{1}{\sqrt3}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find $\sin 30^\circ+\cos 60^\circ$.
7.
Evaluate $\tan 60^\circ$.
8.
If $\sin\theta=\tfrac35$ ($\theta$ acute), find $\cos\theta$.
9.
Evaluate $\sec 0^\circ$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the value of $\sin 75^\circ$.
11.
If $\cos\theta=-\tfrac12$ and $\theta$ lies in the second quadrant, find $\sin\theta$.
12.
Find the value of $\sin 15^\circ$.
13.
Find the value of $\cos 120^\circ$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Prove that $\dfrac{1+\cos\theta}{\sin\theta}+\dfrac{\sin\theta}{1+\cos\theta}=2\csc\theta$.
15.
If $\sin A=\tfrac35$ and $\cos B=\tfrac{9}{41}$ (both acute), find $\sin(A+B)$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $1$
  2. (B) $\tfrac12$
  3. (B) $\csc^2\theta$
  4. (B) $1$
  5. (B) $1$
Section B — Short Answer (2 marks)
  1. $1$.
  2. $\sqrt3$.
  3. $\tfrac45$.
  4. $1$.
Section C — Short Answer (3 marks)
  1. $\tfrac{\sqrt6+\sqrt2}{4}$.
  2. $\tfrac{\sqrt3}{2}$.
  3. $\tfrac{\sqrt6-\sqrt2}{4}$.
  4. $-\tfrac12$.
Section D — Long Answer (5 marks)
  1. Both sides reduce to $2\csc\theta$.
  2. $\tfrac{187}{205}$.
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