PART - 1 CH - 3 Trigonometric Functions - CBSE STD 11 Science Maths Questions - Vidyadip

Question types

PART - 1 CH - 3 Trigonometric Functions question types

65 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

65

Questions

6

Question groups

5

Question types

M.C.Q (1 Marks)

True False[1 Marks ]

1 Marks Question

2 Marks Questions

3 Marks Question

Fill In The Blanks[1 Marks ]

Sample Questions

PART - 1 CH - 3 Trigonometric Functions 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

If $A+B+C=\pi$, then the value of $\tan A+\tan B+$ $\tan C$ is :

A
$\tan \text A \tan \text B +\tan \text B \tan \text C +\tan\text C \tan \text A$
B
$-(\tan A \tan B +\tan B \tan C +\tan C \tan A )$
✓
$\tan A \tan B \tan C$
D
$-\tan A \tan B \tan C$

Answer: C.

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

If $\alpha+\beta+r=2 \pi$, then :

✓
$\tan \frac{\alpha}{2}+\tan \frac{\beta}{2}+\tan \frac{r}{2}=\tan \frac{\alpha}{2} \tan \frac{\beta}{2} \tan \frac{r}{2}$
B
$\tan \frac{\alpha}{2}+\tan \frac{\beta}{2}+\tan \frac{r}{2}=-\tan \frac{\alpha}{2} \tan \frac{\beta}{2} \tan \frac{r}{2}$
C
$\tan \frac{\alpha}{2} \cdot \tan \frac{\beta}{2}+\tan \frac{\beta}{2} \tan \frac{r}{2}+\tan \frac{r}{2} \cdot \tan \frac{\alpha}{2}=1$
D
$\tan \alpha \cdot \tan \beta+\tan \beta \cdot \tan r+\tan r \cdot \tan \alpha=1$

Answer: A.

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

$\cos 15^{\circ}-\sin 15^{\circ}$ is equal to :

A
$-\frac{1}{\sqrt{2}}$
B
$\sqrt{2}$
C
$-\sqrt{2}$
✓
$\frac{1}{\sqrt{2}}$

Answer: D.

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

$\cos 3 A$ is equal to :

A
$3 \cos A-4 \cos ^3 A$
B
$3 \cos A+4 \cos ^3 A$
✓
$4 \cos ^3 A-3 \cos A$
D
None of these

Answer: C.

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

$\sin 3 A$ is equal to :

✓
$3 \sin A-4 \sin ^3 A$
B
$3 \sin A+4 \sin ^3 A$
C
$4 \sin ^3 A-3 \cos A$
D
None of these

Answer: A.

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Q 6True False[1 Marks ]1 Mark

If $\tan \alpha=\frac{x}{x+1}$ and $\tan \beta=\frac{1}{2 x+1}$, then the value of $\alpha+\beta$ is $\frac{\pi}{6}$.

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Q 7True False[1 Marks ]1 Mark

The value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ}$ ________ $\cos 179^{\circ}$ is $1.$

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Q 8True False[1 Marks ]1 Mark

The value of $\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} $ ____________ $\tan 89^{\circ}$ is 1.

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Q 9True False[1 Marks ]1 Mark

$\sin 1^{\circ}<\sin 1$

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Q 10True False[1 Marks ]1 Mark

The maximum value of $\sin (\cos x)$ is 1.

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Q 111 Marks Question1 Mark

Find the value of expression $\left\{\cos A \cdot \cos \left(90^{\circ}- A \right)\right\}$.

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Q 121 Marks Question1 Mark

Write the expression $\frac{2 \tan A}{\tan 2 A}$ in the form of $\tan A$.

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Q 131 Marks Question1 Mark

Write the value of $\sin ^2 24^{\circ}-\sin ^2 6^{\circ}$.

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Q 141 Marks Question1 Mark

If $\tan \alpha=\frac{3}{4}$, then find the value of $\tan 3 \alpha$.

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Q 151 Marks Question1 Mark

Write the value of $\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}$.

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Q 162 Marks Questions2 Marks

Prove that:
$
\sin ^2 \frac{\pi}{18}+\sin ^2 \frac{\pi}{9}+\sin ^2 \frac{7 \pi}{18}+\sin ^2 \frac{4 \pi}{9}=2
$

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Q 172 Marks Questions2 Marks

Prove that:
$
\frac{1+\sin 2 \theta-\cos 2 \theta}{1+\sin 2 \theta+\cos 2 \theta}=\tan \theta
$

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Q 182 Marks Questions2 Marks

Prove for any triangle :
$\begin{array}{l}\tan 2 A \cdot \tan 2 B \cdot \tan 2 C=\tan 2 A+\tan 2 B +\tan 2 C\end{array}$

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Q 192 Marks Questions2 Marks

If $\tan \theta=\frac{a}{b}$, prove that :
$
b \cos 2 \theta+a \sin 2 \theta=b
$

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Q 202 Marks Questions2 Marks

Prove that:
$
\sec \left(\frac{\pi}{4}+\theta\right) \sec \left(\frac{\pi}{4}-\theta\right)=2 \sec 2 \theta
$

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Q 213 Marks Question3 Marks

Prove that:
$
\tan \left(45^{\circ}+\frac{1}{2}\right)=\sqrt{\frac{1+\sin \phi}{1-\sin \phi}}
$

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Q 223 Marks Question3 Marks

If $\tan (A+B)=n \tan (A-B)$ show that :
$
(n+1) \sin 2 B=(n-1) \sin 2 A
$

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Q 233 Marks Question3 Marks

Prove that:
$4 \sin \alpha \cdot \sin \left(\alpha+\frac{\pi}{3}\right) \sin \left(\alpha+\frac{2 \pi}{3}\right)=\sin 3 \alpha$

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Q 24Fill In The Blanks[1 Marks ]1 Mark

$\cos \frac{7 \pi}{8}=$ ________.

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Q 25Fill In The Blanks[1 Marks ]1 Mark

$2 \sin \frac{A}{2} \cos \frac{A}{2}=$ _________.

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Q 26Fill In The Blanks[1 Marks ]1 Mark

The maximum value of $\sin \theta$ is ________.

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Q 27Fill In The Blanks[1 Marks ]1 Mark

$\sin 18^{\circ}=$ _________.

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Q 28Fill In The Blanks[1 Marks ]1 Mark

$\cos \left(-\frac{8 \pi}{3}\right)=$ _________.

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