Introduction of Trigonometry - CBSE STD 10 Maths Questions - Vidyadip

Question types

Introduction of Trigonometry question types

103 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

103

Questions

4

Question groups

5

Question types

M.C.Q (1 Marks)

1 Marks Question

2 Marks Questions

3 Marks Question

Sample Questions

Introduction of Trigonometry questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark

The value of $\cot 10^{\circ} \cot 15^{\circ} \cot 75^{\circ} \cot 80^{\circ}$ is equal to:

A
$0$
B
$2$
✓
$1$
D
cannot be determined

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark

The value of $\sin ^2 30^{\circ}-\cos ^2 30^{\circ}+\tan ^2 45^{\circ}$ is:

A
$\frac{-1}{2}$
B
$\frac{\sqrt{3}}{2}$
✓
$\frac{1}{2}$
D
$0$

Answer: C.

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Q 3M.C.Q (1 Marks)1 Mark

Given that $\sin \theta=\frac{a}{b}$, then $\tan \theta$ is equal to:

A
$\frac{b}{\sqrt{a^2+b^2}}$
B
$\frac{b}{\sqrt{b^2-a^2}}$
C
$\frac{a}{\sqrt{a^2-b^2}}$
✓
$\frac{a}{\sqrt{b^2-a^2}}$

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark

$3 \sin ^2 20^{\circ}-2 \tan ^2 45^{\circ}+3 \sin ^2 70^{\circ}$ is equal to:

A
$0$
✓
$1$
C
$2$
D
$-1$

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark

The maximum value of $\frac{1}{\operatorname{cosec} \theta}$ is

✓
1
B
-1
C
$0$
D
Can't be determined

Answer: A.

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Q 61 Marks Question1 Mark

If $\sin \alpha=\frac{1}{2}$, then find the value of $3 \sin \alpha-4 \sin ^3 \alpha$.

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Q 71 Marks Question1 Mark

If $\tan 2 A=\cot \left(A+60^{\circ}\right)$, find the value of $A$, where $2 A$ is an acute angle.

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Q 81 Marks Question1 Mark

Find the value of $\left(\sec ^2 \theta-1\right) \cdot \cot ^2 \theta$

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Q 91 Marks Question1 Mark

Express $\operatorname{cosec} 48^{\circ}+\tan 88^{\circ}$ in terms of t-ratio of angle 00 and $45^{\circ}$

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Q 101 Marks Question1 Mark

Evaluate: $\sin ^2 A+\cos ^2 A+\cot ^2 A$

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Q 112 Marks Questions2 Marks

$\sin ( A + B )=1\ \&\ \sin (A- B )=\frac{1}{2}$,$0 \leq A + B =90^{\circ}\ \&\ A> B$, then find $A\ \&\ B$.

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Q 122 Marks Questions2 Marks

Find $\operatorname{cosec} 30^{\circ} \cos 60^{\circ}$ geometrically.

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Q 132 Marks Questions2 Marks

Take $A =60$ and $B =30$. Write the value of $\cos A$, $\cos B$ and $\cos (A+B)$. Is $\cos (A+B)=\cos A+\cos B$ ?

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Q 142 Marks Questions2 Marks

Prove the following identity: $\frac{\sin ^4 \theta+\cos ^4 \theta}{1-2 \sin ^2 \theta \cos ^2 \theta}=1$

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Q 152 Marks Questions2 Marks

$\left[\frac{1-\tan A}{1-\cot A}\right]^2=\tan ^2 A ; \angle A$ is acute

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Q 163 Marks Question3 Marks

If $\text{A, B, C}$ are interior angles of a $\triangle \text{A B C}$, then Show that : $\sin \left(\frac{B+C}{2}\right)=\cos \frac{A}{2}$

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Q 173 Marks Question3 Marks

Prove that: $\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}=\frac{1}{\sec \theta-\tan \theta}$

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Q 183 Marks Question3 Marks

Prove the identity: $\frac{1}{\operatorname{cosec} \theta+\cot \theta}-\frac{1}{\sin \theta}=\frac{1}{\sin \theta}-\frac{1}{\operatorname{cosec} \theta-\cot \theta}$

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Q 193 Marks Question3 Marks

If $3 \tan A=4$ then prove that:
(i) $\sqrt{\frac{\sec A-\operatorname{Cosec} A}{\sec A+\operatorname{Cosec} A}}=\frac{1}{\sqrt{3}}$
(ii) $\sqrt{\frac{1-\sin A}{1+\operatorname{Cos} A}}=\frac{1}{2 \sqrt{2}}$

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Q 203 Marks Question3 Marks

Prove that: $(1+\cos \theta-\operatorname{cosec} \theta) \cdot(1+\tan \theta+\sec \theta)=2$

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