Sample QuestionsTrigonometric Equations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The smallest value of $x$ satisfying the equation $\sqrt{3}(\cot\text{x}+\tan\text{x})=4$ is :
- A
$\frac{2\pi}{3}$
- B
$\frac{\pi}{3}$
- ✓
$\frac{\pi}{6}$
- D
$\frac{\pi}{12}$
Answer: C.
View full solution →General solution of $\tan5\text{x}=\cot2\text{x}$ is :
- A
$\frac{\text{n}\pi}{7}+\frac{\pi}{2},\ \text{n}\in\text{Z}$
- B
$\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{3},\ \text{n}\in\text{Z}$
- ✓
$\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{14},\ \text{n}\in\text{Z}$
- D
$\text{x}=\frac{\text{n}\pi}{7}=\frac{\pi}{14},\ \text{n}\in\text{Z}$
Answer: C.
View full solution →The general value of $x$ satisfying the equation $\sqrt{3}\sin\text{x}+\cos\text{x}=\sqrt{3}$ is given by :
- A
$\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{4}+\frac{\pi}{3},\ \text{n}\in\text{Z}$
- ✓
$\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{3}-\frac{\pi}{6},\text{n}\in\text{Z}$
- C
$\text{x}=\text{n}\pi\pm\frac{\pi}{6},\ \text{n}\in\text{Z}$
- D
$\text{x}=\text{n}\pi\pm\frac{\pi}{3},\ \text{n}\in\text{Z}$
Answer: B.
View full solution →If $\cos\text{x}+\sqrt{3}\sin\text{x}=2,\text{then}\ \text{x}=$
- ✓
$\frac{\pi}{3}$
- B
$\frac{2\pi}{3}$
- C
$\frac{4\pi}{3}$
- D
$\frac{5\pi}{3}$
Answer: A.
View full solution →If $\cot\text{x}-\tan\text{x}=\sec\text{x},$ then $,x$ is equal to :
- A
$2\text{n}\pi+\frac{3\pi}{2},\text{n}\in\text{Z}$
- ✓
$\text{n}\pi+(-1)^\text{n}\frac{\pi}{6},\text{n}\in\text{Z}$
- C
$\text{n}\pi+\frac{\pi}{2},\text{n}\in\text{Z}$
- D
Answer: B.
View full solution →Write the number of values of x in $[0,2\pi]$ that satisfy the equation $\sin^2\text{x}-\cos\text{x}=\frac{1}{4}.$
View full solution →Write the number of solutions of the equation $\tan\text{x}+\sec\text{x}=2\cos\text{x}$ in the interval $[0, 2\pi].$
View full solution →Write the values of x in $[0,\pi]$ for which $\sin2\text{x},\frac{1}{2}$ and $\cos2\text{x}$ are in A.P.
View full solution →If $2\sin^2\text{x}=3\cos\text{x},$ where $0\leq\text{x}\leq2\pi,$ then find the value of x.
View full solution →Write the number of points of intersection of the curves $2\text{y}=1$ and $\text{y}=\cos\text{x},0\leq\text{x}\leq2\pi.$
View full solution →Find the general solutions of the following equations:
$\tan\text{x}=-\frac{-1}{\sqrt{3}}$
View full solution →Find the general solutions of the following equations:
$\sqrt{3}\sec\text{x}=2$
View full solution →Find the general solutions of the following equations:
$\cos3\text{x}=\frac{1}{2}$
View full solution →Find the general solutions of the following equations:$\text{cosec }\text{x}=-\sqrt{2}$
View full solution →Find the general solutions of the following equations:
$\sec\text{x}=\sqrt{2}$
View full solution →Find the general solutions of the following equations:
$\sin2\text{x}=\cos3\text{x}$
View full solution →Solve the following equations:
$(\sqrt{3}-1)\cos\text{x}+(\sqrt{3}+1)\sin\text{x}=2$
View full solution →Find the general solutions of the following equations:
$\sin2\text{x}+\cos\text{x}=0$
View full solution →Find the general solutions of the following equations:
$\tan\text{px}=\cot\text{qx}$
View full solution →Solve the following equations: $\cos\text{x}+\cos3\text{x}-\cos2\text{x}=0$
View full solution →Find the general solutions of the following equations:
$\cos4\text{x}=\cos2\text{x}$
View full solution →Find the general solutions of the following equations:
$3\cos^{2}\text{x}-2\sqrt{3}\sin\text{x}\cos\text{x}-3\sin^{2}\text{x}=0$
View full solution →Solve the following equations:
$\sin2\text{x}-\sin4\text{x}+\sin6\text{x}=0$
View full solution →Solve the following equation:
$2\cos^{2}\text{x}-5\cos\text{x}+2=0$
View full solution →Solve the following equations:
$\cot\text{x}+\tan\text{x}=2$
View full solution →Solve the following equations:
$\cos\text{x}+\sin\text{x}=\cos2\text{x}+\sin2\text{x}$
View full solution →Solve the following equations:
$\sin\text{x}\ \tan\text{x}-1\tan\text{x}-\sin\text{x}$
View full solution →Solve the following equations:
$3\sin2\text{x}-5 \sin\text{x}\cos \text{x} + 8 \cos2\text{x = 2}$
View full solution →Solve the following equations:
$\sin\text{x}-3\sin2\text{x}+\sin3\text{x}=\cos\text{x}-3\cos2\text{x}+\cos3\text{x}$
View full solution →Solve the following equations:
$4\sin\text{x}\cos\text{x}+2\sin\text{x}+2\cos\text{x}+1=0$
View full solution →