Vidaara.orgClass 10 · Mathematics
CodeVID-M10-09-TRI-01
Trigonometric Ratios & Identities — Assignment
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.
$\sin\theta=$
- A.$\tfrac{\text{adj}}{\text{hyp}}$
- B.$\tfrac{\text{opp}}{\text{hyp}}$
- C.$\tfrac{\text{opp}}{\text{adj}}$
- D.$\tfrac{\text{hyp}}{\text{opp}}$
2.
$\cos\theta=$
- A.$\tfrac{\text{adj}}{\text{hyp}}$
- B.$\tfrac{\text{opp}}{\text{hyp}}$
- C.$\tfrac{\text{opp}}{\text{adj}}$
- D.$\tfrac{1}{\sin\theta}$
3.
$\tan\theta=\dfrac{\sin\theta}{?}$
- A.$\cos\theta$
- B.$\sin\theta$
- C.$1$
- D.$\sec\theta$
4.
$\sin^2\theta+\cos^2\theta=$
- A.$0$
- B.$1$
- C.$2$
- D.$\tan^2\theta$
5.
$1+\tan^2\theta=$
- A.$\sec^2\theta$
- B.$\csc^2\theta$
- C.$\cot^2\theta$
- D.$1$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
If $\sin\theta=\tfrac35$ ($\theta$ acute), find $\cos\theta$.
7.
If $\tan\theta=1$, find $\theta$.
8.
Simplify $\sin^2 30^\circ+\cos^2 30^\circ$.
9.
Find $\csc\theta$ if $\sin\theta=\tfrac12$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
If $\tan\theta=\tfrac43$, find $\sin\theta$ and $\cos\theta$.
11.
Show that $1-\cos^2\theta=\sin^2\theta$ and verify at $\theta=30^\circ$.
12.
If $\sec\theta=\tfrac{13}{12}$, find $\tan\theta$.
13.
Simplify $(1+\tan^2\theta)\cos^2\theta$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Prove that $\dfrac{\sin\theta}{1+\cos\theta}+\dfrac{1+\cos\theta}{\sin\theta}=2\csc\theta$.
15.
If $\sin\theta+\cos\theta=\sqrt2\cos\theta$, show that $\tan\theta=\sqrt2-1$.
Answer Key
Section A — Multiple Choice Questions
- (B) $\tfrac{\text{opp}}{\text{hyp}}$
- (A) $\tfrac{\text{adj}}{\text{hyp}}$
- (A) $\cos\theta$
- (B) $1$
- (A) $\sec^2\theta$
Section B — Short Answer (2 marks)
- $\tfrac45$.
- $45^\circ$.
- $1$.
- $2$.
Section C — Short Answer (3 marks)
- $\sin\theta=\tfrac45,\ \cos\theta=\tfrac35$.
- Both equal $\tfrac14$.
- $\tfrac{5}{12}$.
- $1$.
Section D — Long Answer (5 marks)
- $=2\csc\theta$.
- $\tan\theta=\sqrt2-1$.
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