Vidaara.orgClass 10 · Mathematics
CodeVID-M10-09-STD-01
Standard Angles — 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.
$\sin 30^\circ=$
- A.$\tfrac12$
- B.$\tfrac{\sqrt3}{2}$
- C.$1$
- D.$0$
2.
$\cos 60^\circ=$
- A.$\tfrac{\sqrt3}{2}$
- B.$\tfrac12$
- C.$1$
- D.$0$
3.
$\tan 45^\circ=$
- A.$0$
- B.$1$
- C.$\sqrt3$
- D.$\tfrac{1}{\sqrt3}$
4.
$\sin 90^\circ=$
- A.$0$
- B.$\tfrac12$
- C.$1$
- D.$\sqrt3$
5.
$\cos 0^\circ=$
- A.$0$
- B.$1$
- C.$\tfrac12$
- D.$\infty$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Evaluate $\sin 30^\circ+\cos 60^\circ$.
7.
Evaluate $\tan 60^\circ$.
8.
Evaluate $2\sin 45^\circ\cos 45^\circ$.
9.
Evaluate $\sin^2 60^\circ+\cos^2 60^\circ$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Evaluate $\sin 30^\circ\cos 60^\circ+\cos 30^\circ\sin 60^\circ$.
11.
Evaluate $\dfrac{\tan 45^\circ+1}{\sec 60^\circ}$.
12.
Evaluate $\tan^2 60^\circ+2\tan^2 45^\circ$.
13.
Evaluate $\sin 60^\circ\cos 30^\circ-\cos 60^\circ\sin 30^\circ$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Evaluate $2\sin^2 30^\circ-3\cos^2 45^\circ+\tan^2 60^\circ$.
15.
If $\tan(A+B)=\sqrt3$ and $\tan(A-B)=\tfrac{1}{\sqrt3}$ (with $A>B$, $A+B\le90^\circ$), find $A$ and $B$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\tfrac12$
- (B) $\tfrac12$
- (B) $1$
- (C) $1$
- (B) $1$
Section B — Short Answer (2 marks)
- $1$.
- $\sqrt3$.
- $1$.
- $1$.
Section C — Short Answer (3 marks)
- $1$.
- $1$.
- $5$.
- $\tfrac12$.
Section D — Long Answer (5 marks)
- $2$.
- $A=45^\circ,\ B=15^\circ$.
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