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.
If $\text{cosec x}+\cot \text{x}=\frac{11}{2},$ then $\tan\text{x}$ is equal to:
- A
$\frac{21}{22}$
- B
$\frac{15}{16}$
- ✓
$\frac{44}{117}$
- D
$\frac{117}{44}$
Answer: C.
View full solution →$\sec^2\text{x}=\frac{4\text{xy}}{(\text{x}+\text{y})^2}$ is true if and only if
Answer: B.
View full solution →If A lies in second quadrant $3\tan\text{A}+4=0,$ then the value of $2\cot\text{A}-5\cot\text{A}+\sin\text{A}$ is:
- A
$-\frac{53}{10}$
- ✓
$\frac{23}{10}$
- C
$\frac{37}{10}$
- D
$\frac{7}{10}$
Answer: B.
View full solution →If $\text{cosec x}+\cot\text{x}=\frac{11}{2},$ then $\tan\text{x}=$
- A
$\frac{21}{22}$
- B
$\frac{15}{16}$
- ✓
$\frac{44}{117}$
- D
$\frac{117}{43}$
Answer: C.
View full solution →The value of $\sin^25^\circ+\sin^210^\circ+\sin^215^\circ+\ ...\ +\sin^285^\circ+\sin^290^\circ$ is:
Answer: C.
View full solution →If $\tan\text{A}+\cot\text{A}=4,$ then write the value of $\tan^4\text{A}+\cot^4\text{A}.$
View full solution →Write the maximum and minimum values of $\cos(\cos\text{x}).$
View full solution →Write the value of $2(\sin^6\text{x}+\cos^6\text{x})-3(\sin^4\text{x}+\cos^4\text{x})+1.$
View full solution →If $\sin\text{x}=\text{cosec}\text{ x}=2,$ then write the value of $\sin^\text{n}\text{x}\text{+ cosec}^\text{n}\text{ x}.$
View full solution →If $\sin^2\text{x}+\sin^2\text{ x}=1,$ then write the value of $\cos^8\text{x}+2\cos^6\text{x}+\cos^4\text{ x}.$
View full solution →Prove that: $\tan(-225^\circ)\cot(-405^\circ)-\tan(765^\circ)+\cot(675^\circ)=0$
View full solution →Find x From the following equation: $\text{ x}\cot\Big(\frac{\pi}{2}+\theta\Big)+\tan\Big(\frac{\pi}{2}\Big)\sin\theta=\text{coses}\Big(\frac{\pi}{2}+\theta\Big)=0$
View full solution →Find the value of the following trigonomentric ratio: $\cos\Big(\frac{39\pi}{4}\Big)$
View full solution →If A, B, C, D be the angles of a cyclic quadrilateral, take in order, proved that: $\cos(180^\circ-\text{A})+\cos(180^\circ+\text{B})+\cos(180^\circ+\text{C})-\sin(90^\circ+\text{D})=0$
View full solution →Prove that: $\sin\frac{10\pi}{3}\cos\frac{13\pi}{6}+\cos\frac{8\pi}{3}\sin\frac{5\pi}{6}=-1$
View full solution →Find the values of the other five trigonometric functions in the following: $\sin\text{x}=\frac{3}{5},$ x in quadrant I
View full solution →Prove that: $3\sin\frac{\pi}{6}\sec\frac{\pi}{3}-4\sin\frac{5\pi}{6}\cot\frac{\pi}{4}=1$
View full solution →Prove the following identities: $1-\frac{\sin^2\text{x}}{1+\cot\text{x}}-\frac{\cos^2\text{x}}{1+\tan\text{x}}=\sin\text{x}\cos\text{x}$
View full solution →If $\tan\text{x}=\frac{\text{a}}{\text{b}},$ show that $\frac{\text{x}\sin\text{x - b}\cos\text{x}}{\text{a}\sin\text{x}+\text{b}\cos\text{x}}=\frac{\text{a}^2-\text{b}^2}{\text{a}^2+\text{b}^2}.$
View full solution →Prove that: $\frac{\sin(\pi+\text{x})\cos\big(\frac{\pi}{2}+\text{x}\big)\tan\big(\frac{3\pi}{2}-\text{x}\big)\cot(2\pi-\text{x})}{\sin(2\pi-\text{x})\cos(2\pi+\text{x})\text{cosec}(-\text{x})\sin\big(\frac{3\pi}{2}-\text{x}\big)}=1$
View full solution →If $\text{T}_\text{n}=\sin^\text{n}\text{x}+\cos^\text{n}\text{x},$ Prove that $\frac{\text{T}_3-\text{T}_5}{\text{T}_1}=\frac{\text{T}_5-\text{T}_7}{\text{T}_3}$
View full solution →If $\text{T}_\text{n}=\sin^\text{n}\text{x}+\cos^\text{n}\text{x},$ Prove that $6\text{T}_{10}-15\text{T}_8+10\text{T}_6-1=0$
View full solution →If $\text{T}_\text{n}=\sin^\text{n}\text{x}+\cos^\text{n}\text{x},$ Prove that $2 \text{T}_6 - 3\text{ T}_4 + 1 = 0$
View full solution →Prove that $\Bigg|\sqrt{\frac{1-\sin\text{x}}{1+\sin\text{x}}}+\sqrt{\frac{1+\sin\text{x}}{1-\sin\text{x}}}\Bigg|$ $=-\frac{2}{\cos\text{x}},$ where $\frac{\pi}{2}<\text{x}<\pi$
View full solution →Prove the following identities: $\Big(\frac{1}{\sec^2\text{x}-\cos^\text{x}}+\frac{1}{\text{Cosec}^2\text{x}-\sin^2\text{x}}\Big)\sin^2\text{x}\cos^2\text{x}=\frac{1-\sin^2\text{x}\cos^2\text{x}}{2+\sin^2\text{x}\cos^2\text{x}}$
View full solution →