Sample QuestionsTrigonometric Identities questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}$ is equal to:
- A
$\sec^2\text{A}$
- B
$-1$
- C
$\cot^2\text{A}$
- ✓
$\tan^2\text{A}$
Answer: D.
View full solution →$2(\sin^6\theta+\cos^6\theta)-3(\sin^4\theta+\cos^4\theta)$ is equal to:
Answer: C.
View full solution →If $\text{a}\cos\theta+\text{b}\sin\theta=4\text{ and a}\sin\theta-\text{b}\cos\theta=3,$ then $a^2+b^2=0$
Answer: C.
View full solution →If $\text{x}=\text{r}\sin\theta\cos\phi,\text{y}=\text{r}\sin\phi$ and ${z}=\text{r}\cos\theta,$ then:
- ✓
$x^2+y^2+z^2=r^2$
- B
$x^2+y^2-z^2=r^2$
- C
$x^2-y^2+z^2=r^2$
- D
$z^2+y^2-x^2=r^2$
Answer: A.
View full solution →$(\sec\text{A}+\tan\text{A})(1-\sin\text{A})=$
- A
$\sec\text{A}$
- B
$\sin\text{A}$
- C
$\text{cosec A}$
- ✓
$\cos\text{A}$
Answer: D.
View full solution →Write 'True' or 'False' and justify your answer in the following:
The value of $\sin\theta+\cos\theta$ is always greater than 1.
View full solution →Write 'True' or 'False' and justify your answer in the following:
The value of the expression $\sin80^\circ-\cos80^\circ$ is negative.
View full solution →Write 'True' or 'False' and justify your answer in the following:
$\cos\theta=\frac{\text{a}^2+\text{b}^2}{2\text{ab}}$, where a and b are two lab distinct numbers such that ab > 0.
View full solution →Write 'True' or 'False' and justify your answer in the following:
The value of $\sin\theta$ is $\text{x}+\frac{1}{\text{x}},$ where 'x' is a positive real number.
View full solution →Write 'True' or 'False' and justify your answer in the following:
The value of $\cos^2{23}-\sin^2{67}$ is positive.
View full solution →Prove the following trigonometric identities.
$\text{cos}^2\text{A}+\frac{1}{1+\cot^2\text{A}}=1$
View full solution →Prove the following trigonometric identities.
$\sin^2\text{A}\cot^2\text{A}+\cos^2\text{A}\tan^2\text{A}=1$
View full solution →What is the value of $\frac{\tan^2\theta-\sec^2\theta}{\cot^2\theta-\text{cosec}^2\theta}?$
View full solution →Prove the following trigonometric identities.
$(1+\tan^2\theta)(1-\sin\theta)(1+\sin\theta)=1$
View full solution →Prove the following trigonometric identities.
$\frac{1+\cos\theta-\sin^2\theta}{\sin\theta(1+\cos\theta)}=\cot\theta$
View full solution →Prove the following trigonometric identities.
$\frac{1+\cos\theta+\sin\theta}{1+\cos\theta-\sin\theta}=\frac{1+\sin\theta}{\cos\theta}$
View full solution →If $\cos\text{A}=\frac{7}{25},$ find is the value of $\tan\text{A}+\cot\text{A}$.
View full solution →Prove the following trigonometric identities.
$\frac{\cot\text{A}+\tan\text{B}}{\cot\text{B}+\tan\text{A}}=\cot\text{A}\tan\text{B}$
View full solution →If $\cot\theta=\frac{1}{\sqrt{3}},$ find the value of $\frac{1+\cos^2\theta}{2-\sin^2\theta}$.
View full solution →If $\text{cosec A}=\sqrt{2},$ find the value of $\frac{2\sin^2\text{A}+3\cot^2\text{A}}{4(\tan^2-\cos^2\text{A})}$.
View full solution →Prove the following trigonometric identities.
$\frac{\sin\text{A}}{\sec\text{A}+\tan\text{A}-1}+\frac{\cos\text{A}}{\text{cosec A}+\cot\text{A}-1}=1$
View full solution →Prove the following trigonometric identities.
$\frac{\cot^2\text{A}(\sec\text{A}-1)}{1+\sin\text{A}}=\sec^2\text{A}\Big(\frac{1-\sin\text{A}}{1+\sin\text{A}}\Big)$
View full solution →Prove the following trigonometric identities.
$\frac{\tan^2\text{A}}{1+\tan^2\text{A}}+\frac{\cot^2\text{A}}{1+\cot^2\text{A}}=1$
View full solution →Prove the following trigonometric identities.
If $\text{T}_\text{n}=\sin^\text{n}\theta+\cos^\text{n}\theta,$ porve that $\frac{\text{T}_3-\text{T}_5}{\text{T}_1}=\frac{\text{T}_5-\text{T}_7}{\text{T}_3}.$
View full solution →Prove the following trigonometric identities.
$(\text{cosec }\theta-\sec\theta)(\cot\theta-\tan\theta)=(\text{cosec }\theta+\sec\theta)(\sec\theta\text{ cosec }\theta-2)$
View full solution →