Sample QuestionsIntroduction to Trigonometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\frac { 1 + \tan ^ { 2 } A } { 1 + \cot ^ { 2 } A }=$
- A
$sec^2A$
- B
$–1$
- C
$cot^2A$
- ✓
$tan^2A$
Answer: D.
View full solution →$(sec A + tan A) (1 – sin A)$
- A
$sec A$
- B
$sin A$
- C
$cosec A$
- ✓
$cos A$
Answer: D.
View full solution →$(1 +$ $tan $$\theta$ $+ sec$ $\theta$$) (1 + cot$$\theta$ $– cosec$$\theta$) =
Answer: C.
View full solution →$9\ sec^2 A – 9$ $tan^2 A =$
Answer: A.
View full solution →$\tan 30^{\circ} \cdot \tan 60^{\circ}=$ _______
- A
$\sqrt{3}$
- B
$\frac{1}{\sqrt{3}}$
- C
$0$
- ✓
$1$
Answer: D.
View full solution →If the value of $\theta$ is increased then value of $\sin \theta$ is _______ (increased, decreased, minus) $\quad$
View full solution →$\left(1+\tan ^2 45^{\circ}\right)=$ _______ (1,0,2)
View full solution →_______ is the short form of cosecant $A$. $(\cos A, \operatorname{cosec} A, \sec A)$
View full solution →If value of $\theta$ Is increased Then Value of $\cos \theta$ is _______ (increase, decrease, minus)
View full solution →For an angle $\theta$ the value of $\sin \theta$ ........ when the value of theta increases. (increase, decrease, negative)
View full solution →$\cot A$ is undefined for $A=0^{\circ}$.
View full solution →$\sin \theta=\cos \theta$ for all values of $\theta$.
View full solution →As the value of $\theta$ increases, the value of $\cos \theta$ increases.
View full solution →The value of $\sin \theta$ increases as the value of $\theta$ increases.
View full solution →$\sin ( A + B )=\sin A +\sin B$.
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $(cosec A - sin A) (sec A - cos A) =$ $\frac { 1 } { \tan A + \cot A }$
$[$Hint: Simplify $LHS$ and $RHS$ separately$]$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\sqrt { \frac { 1 + \sin A } { 1 - \sin A } }$ $= sec A + tan A$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\frac { 1 + \sec A } { \sec A } = \frac { \sin ^ { 2 } A } { 1 - \cos A }$
$[$Hint: Simplify $LHS$ and $RHS$ separately$]$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined.
$\left( \frac { 1 + \tan ^ { 2 } A } { 1 + \cot ^ { 2 } A } \right) = \left( \frac { 1 - \tan A } { 1 - \cot A } \right) ^ { 2 } = tan^2 A$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $( cosec\; \theta - \cot \theta ) ^ { 2 } = \frac { 1 - \cos \theta } { 1 + \cos \theta }$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\frac { \sin \theta - 2 \sin ^ { 3 } \theta } { 2 \cos ^ { 2 } \theta - \cos \theta } = \tan \theta$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined.
$\frac { \cos A } { 1 + \sin A } + \frac { 1 + \sin A } { \cos A } = 2 \sec A$
View full solution →If $\tan (A + B) =$ $\sqrt3$ and $\tan (A - B) =$ $\frac{1}{\sqrt3}$; $0^\circ < A + B$ $\leq$ $90^\circ ; A > B$, then find $A$ and $B$.
View full solution →Evaluate: $\frac { 5 \cos ^ { 2 } 60 ^ { \circ } + 4 \sec ^ { 2 } 30 ^ { \circ } - \tan ^ { 2 } 45 ^ { \circ } } { \sin ^ { 2 } 30 ^ { \circ } + \cos ^ { 2 } 30 ^ { \circ } }$
View full solution →Evaluate: $\frac{\sin 30^{\circ}+\tan 45^{\circ}-\ cosec 60^{\circ} }{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}$
View full solution →Prove the given identities, where the angles involved are acute angles for which the expressions are defined.$(\sin A+ cosec\ A)^2+(\cos A+\sec A)^2=7+\tan ^2 A+\cot ^2 A$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined.$\frac{\cos A-\sin A+1}{\cos A+\sin A-1} = cosec\ A + \cot A$, using the identity $\operatorname{cosec}^2 \mathrm{~A}=1+\cot ^2 \mathrm{~A}$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined.$ \frac{{\tan A }}{{1 - \cot A }} + \frac{{\cot A }}{{1 - \tan A }} = 1 + \sec A \ cosec\ A$
$[$Hint: Write the expression in terms of $\sin \theta$ and $\cos \theta]$
View full solution →Write all the other trigonometric ratios of $\angle A$ in terms of $\sec A.$
View full solution →Express the trigonometric ratios $\sin \mathrm{A}, \sec \mathrm{A}$ and $\tan \mathrm{A}$ in terms of $\cot \mathrm{A}$.
View full solution →| A | B |
| Q.1. $\sqrt{3}=$...... | (a) $60^{\circ}$ |
| Q.2. In a right triangle $ABC \angle B$ is a right angle $AC =20$ and $B =10$ then $\angle ACB =$...... | (b) 0.54 |
| (c) 1.73 |
| A | B |
| Q.1. $\tan 45^{\circ}-\cot 45^{\circ}=\ldots \ldots .$. | (a) $0$ |
| Q.2. $\tan 30^{\circ}$ ...... and have equal values | (b) 1 |
| | (c) $\cot 60^{\circ}$ |
| A | B |
| Q.1. The value of ......... is not undefined. | (a) $\tan 90^{\circ}$ |
| Q.2. ....... have equal values. | (b) $\tan 0^{\circ}$ |
| | (c) $\sin 60^{\circ}$ and $\cos 30^{\circ}$ |
| A | B |
| Q.1. The value of ....... is zero. | (a) $\tan 90^{\circ}$ |
| Q.2. The value of ....... is undefined. | (b) $\cos 90^{\circ}$ |
| | (c) $\cot 90^{\circ}$ |
| A | B |
| Q.1. Which of the following has value 1 ? | (a) $\tan ^2 \theta+\sec ^2 \theta$ |
| Q.2. Which has the value -1 ? | (b) $\operatorname{cosec}^2 \theta-\cot ^2 \theta$ |
| | (c) $\tan ^2 \theta-\sec ^2 \theta$ |