Sample QuestionsTrigonometric Functions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The value of $\sin50^\circ-\sin70^\circ+\sin10^\circ$ is equal to:
- A
$1$
- ✓
$0$
- C
$\frac{1}{2}$
- D
$2$
Answer: B.
View full solution →If $\tan\theta=3$ and $\theta$ lies in third quadrant, then the value of $\sin\theta$ is:
- A
$\frac{1}{\sqrt{10}}$
- B
$-\frac{1}{\sqrt{10}}$
- ✓
$\frac{-3}{\sqrt{10}}$
- D
$\frac{3}{\sqrt{10}}$
Answer: C.
View full solution →If A lies in the second quadrant and $3\tan\text{A}+4=0,$ then the value of $2\cot\text{A}-5\cos\text{A}+\sin\text{A}$ is equal to:
- A
$\frac{-53}{10}$
- ✓
$\frac{23}{10}$
- C
$\frac{37}{10}$
- D
$\frac{7}{10}$
Answer: B.
View full solution →The value of $\tan1^\circ\tan2^\circ\tan3^\circ...\tan89^\circ$ is:
Answer: B.
View full solution →The value of $\sin(45^\circ+\theta)-\cos(45^\circ-\theta)$ is:
- A
$2\cos\theta$
- B
$2\sin\theta$
- C
$1$
- ✓
$0$
Answer: D.
View full solution →If $\tan\theta+\tan2\theta+\sqrt{3}\tan\theta\tan2\theta=\sqrt{3},$ then $\theta=\frac{\text{n}\pi}{3}+\frac{\pi}{9}$
View full solution →$\sin10^\circ$ is greater than $\cos10^\circ.$
View full solution →One value of $\theta$ which satisfies the equation $\sin^4\theta-2\sin^2\theta-1$ lies between 0 and $2\pi.$
View full solution →If $\tan\text{A}=\frac{1-\cos\text{B}}{\sin\text{B}},$ then $\tan2\text{A}=\tan\text{B}$
View full solution →The equality $\sin\text{A}+\sin2\text{A}+\sin3\text{A}=3$ holds for some real value of A.
View full solution →If $\sin\theta+\cos\theta=1,$ then find the general value of $\theta$
View full solution →If $\tan(\text{A + B})=\text{p},\tan(\text{A}-\text{B})=\text{q},$ then show that $\tan2\text{A}=\frac{\text{p + q}}{1-\text{pq}}$
$\big[$Hint: Use $2\text{A}=(\text{A + B})+(\text{A}-\text{B})\big]$
View full solution →Prove that $4\text{A}=4\sin\text{A}\cos^3\text{A}-4\cos\text{A}\sin^3\text{A}.$
View full solution →If $2\sin^2\theta=3\cos\theta,$ where $0\leq\theta\leq2\pi,$ then find the value of $\theta.$
View full solution →Find the value of $\tan22^{\circ}30'.$
View full solution →If $\text{a}\cos\theta+\text{b}\sin\theta=\text{m}$ and $\text{a}\sin\theta-\text{b}\cos\theta=\text{n},$ then show that $\text{a}^2+\text{b}^2=\text{m}^2+\text{n}^2.$
View full solution →Prove that $\frac{\tan\text{A}+\sec\text{A}-1}{\tan\text{A}-\sec\text{A}+1}=\frac{1+\sin\text{A}}{\cos\text{A}}$
View full solution →Prove that $\cos\theta\cos\frac{\theta}{2}-\cos3\theta\cos\frac{9\theta}{2}=\sin7\theta\sin8\theta$
$\Big[$Hint: Express $\text{L.H.S.}=\frac{1}{2}\Big[2\cos\theta\cos\frac{\theta}{2}-2\cos3\theta\cos\frac{9\theta}{2}\Big]\Big]$
View full solution →If $\frac{\sin(\text{x+y})}{\sin(\text{x}-\text{y})}=\frac{\text{a+b}}{\text{a}-\text{b}},$ then show that $\frac{\tan\text{x}}{\tan\text{y}}=\frac{\text{a}}{\text{b}}.$
[Hint: Use Componendo and Dividendo]
View full solution →Find the general solution of the equation $\sin\text{x}-3\sin2\text{x}+\sin3\text{x}=\cos\text{x}-3\cos2\text{x}+\cos3\text{x}$
View full solution →If $\text{k}=\sin\Big(\frac{\pi}{18}\Big)\sin\Big(\frac{5\pi}{18}\Big)\sin\Big(\frac{7\pi}{18}\Big),$ then the numerical value of k is _______.
View full solution →The maximum distance of a point on the graph of the function $\text{y}=\sqrt{3}\sin\text{x}+\cos\text{x}$ from x-axis is _______.
View full solution →$3(\sin\text{x}-\cos\text{x})^4+6(\sin\text{x}+\cos\text{x})^2+4(\sin^6\text{x}+\cos^6\text{x})=$ _______.
View full solution →In a triangle ABC with $\angle\text{C}=90^\circ$ the equation whose roots are tan A and tan B is _______.
[Hint: $\text{A + B}=90^\circ\Rightarrow\tan\text{A}\tan\text{B}=1$ and $\tan\text{A}+\tan\text{B}=\frac{2}{\sin2\text{A}}$ ]
View full solution →If $\sin\text{x}+\cos\text{x}=\text{a},$ then,
- $\sin^6\text{x}+\cos^6\text{x}=............$
- $|\sin\text{x}-\cos\text{x}|=..............$
View full solution →In the following match each item given under the $\text{column}\ C_1$ to its correct answer given under the $\text{column}\ C_2$:
| |
$\text{column}\ C_1$ |
|
$\text{column}\ C_2$ |
| $(a)$ |
$\sin(\text{x + y})\sin\text{x}-\text{y}$ |
$(i)$ |
$\cos^2\text{x}-\sin^2\text{y}$ |
| $(b)$ |
$\cos(\text{x + y})\cos(\text{x}-\text{y})$ |
$(ii)$ |
$\frac{1-\tan\theta}{1+\tan\theta}$ |
| $(c)$ |
$\cot\Big(\frac{\pi}{4}+\theta\Big)$ |
$(iii)$ |
$\frac{1+\tan\theta}{1-\tan\theta}$ |
| $(d)$ |
$\tan\Big(\frac{\pi}{4}+\theta\Big)$ |
$(iv)$ |
$\sin^2\text{x}-\sin^2\text{y}$ |
View full solution →Find the value of the expression $\cos^4\frac{\pi}{8}+\cos^4\frac{3\pi}{8}+\cos^4\frac{5\pi}{8}+\cos^4\frac{7\pi}{8}$
[Hint: Simplify the expression to $2\Big(\cos^4\frac{\pi}{8}+\cos^4\frac{3\pi}{8}\Big)=2\Big[\Big(\cos^2\frac{\pi}{8}+\cos^2\frac{3\pi}8{}\Big)^2-2\cos^2\frac{\pi}{8}\cos^2\frac{3\pi}{8}\Big]$
View full solution →If $\text{x}=\sec\phi-\tan\phi$ and $\text{y}=\text{cosec}\phi+\cot\phi$ then show that $\text{xy}+\text{x}-\text{y}+1=0$
[Hint: Find xy + 1 and then show that x - y = -(xy + 1)]
View full solution →If $\cos\alpha+\cos\beta=0=\sin\alpha+\sin\beta,$ then prove that $\cos2\alpha+\cos2\beta=-2\cos(\alpha+\beta).$
$\big[$Hint: $(\cos\alpha+\cos\beta)^2-(\sin\alpha+\sin\beta)^2=0\big]$
View full solution →Find the general solution of the equation $5\cos^2\theta+7\sin^2\theta-6=0$
View full solution →