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.
$\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ=?$
- A
$\sqrt{3}$
- B
$\frac{1}{\sqrt{3}}$
- C
$-1$
- ✓
$1$
Answer: D.
View full solution →If $\sec\theta=\frac{25}{7}$ then $\sin\theta=?$
- A
$\frac{7}{24}$
- B
$\frac{24}{7}$
- ✓
$\frac{24}{25}$
- D
Answer: C.
View full solution →If $3\cot\theta=4$ then $\frac{(5\sin\theta+3\cos\theta)}{(5\sin\theta-3\cos\theta)} =?$
- A
$\frac{1}{3}$
- B
$3$
- C
$\frac{1}{9}$
- ✓
$9$
Answer: D.
View full solution →If $7\tan\theta=4$ then $\frac{(7\sin\theta-3\cos\theta)}{(7\sin\theta+3\cos\theta)} =?$
- ✓
$\frac{1}{7}$
- B
$\frac{5}{7}$
- C
$\frac{3}{7}$
- D
$\frac{5}{14}$
Answer: A.
View full solution →If $\cos\theta=\frac{4}{5}$ then $\tan\theta=?$
- ✓
$\frac{3}{4}$
- B
$\frac{4}{3}$
- C
$\frac{3}{5}$
- D
$\frac{5}{3}$
Answer: A.
View full solution →Very-Short and Short-Answer Questions.
Find the value of $\sin48^\circ\sec42^\circ+\cos48^\circ\text{cosec }42^\circ.$
View full solution →Very-Short and Short-Answer Qustions:
If $\cos\theta=\frac23,$ write the value of $\big(4+4\tan^2\theta\big).$
View full solution →Very-Short and Short-Answer Qustions:
If $\cot\text{A}=\frac43$ and $(\text{A}+\text{B})=90^\circ,$ what is the value of $\sin\text{B}?$
View full solution →Prove the following identities:
$\cot^2\theta-\frac{1}{\sin^2\theta}=-1$
View full solution →Prove that $\sqrt{\frac{1+\cos\text{A}}{1-\cos\text{A}}}=(\text{cosec A}+\cot\text{A}).$
View full solution →Very-Short and Short-Answer Questions.If $5\text{x}=\sec\theta$ and $\frac{5}{\text{x}}=\tan\theta,$ find the value of $5\Big(\text{x}^2-\frac{1}{\text{x}^2}\Big).$
View full solution →Prove the following identities:
$\frac{1-\tan^2\theta}{\cot^2-1}=\tan^2\theta$
View full solution →Very-Short and Short-Answer Qustions:
Write the value of $\big(1+\tan^2\theta\big)\big(1+\sin\theta\big)\big(1-\sin\theta\big).$
View full solution →Prove the following identities:
$\frac{\cos\theta}{(1-\tan\theta)}+\frac{\sin^2\theta}{(\cos\theta-\sin\theta)}=(\cos\theta+\sin\theta)$
View full solution →Prove the following identities:
$1+\frac{\tan^2\theta}{(1+\sec\theta)}=\sec\theta$
View full solution →Prove the following identities:
$\frac{\tan\theta}{(\sec\theta-1)}+\frac{\tan\theta}{(\sec\theta+1)}=2\text{cosec}\theta$
View full solution →Prove the following identities:
$(1+\tan\theta+\cot\theta)(\sin\theta-\cos\theta)=\Big(\frac{\sec\theta}{\text{cosec}^2\theta}-\frac{\text{cosec}\theta}{\sec^2\theta}\Big)$
View full solution →Prove the following identities:
If $1+\sin^2\theta=3\sin\theta\cos\theta$ then prove that $\tan\theta=1$ or $\frac12.$
View full solution →Prove the following identities:
$\frac{1-\tan^2\theta}{1+\tan^2\theta}=\big(\cos^2\theta-\sin^2\theta\big)$
View full solution →Prove the following identities:
$\frac{\sec\theta-\tan\theta}{\sec\theta+\tan\theta}=\frac{\sin^2\theta}{(1+\cos\theta)^2}$
View full solution →Prove the following identities:
$\frac{\tan\text{A}+\tan\text{B}}{\cot\text{A}+\cot\text{B}}=\tan\text{A}\tan\text{B}$
View full solution →If $\Big(\frac{\text{x}}{\text{a}}\sin\theta-\frac{\text{y}}{\text{b}}\cos\theta\Big)=1$ and $\Big(\frac{\text{x}}{\text{a}}\cos\theta+\frac{\text{y}}{\text{b}}\sin\theta\Big)=1,$ prove that $\Big(\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}\Big)=2.$
View full solution →If $(\tan\theta+\sin\theta)=\text{m}$ and $(\tan\theta-\sin\theta)=\text{n},$ prove that $\big(\text{m}^2-\text{n}^2\big)^2=16\text{mn}.$
View full solution →If $\sec\theta+\tan\theta=\text{p},$ prove that:$\sec\theta=\frac12\Big(\text{p}+\frac{1}{\text{p}}\Big)$
View full solution →If $(\text{cosec }\theta+\sin\theta)=\text{a}^3$ and $(\sec\theta-\cos\theta)=\text{b}^3,$ prove that $\big(\text{a}^2\text{b}^2\big)\big(\text{a}^2+\text{b}^2\big)=1.$
View full solution →