M.C.Q (1 Marks)

MCQ 11 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

Correct option: C.

$\tan A \tan B \tan C$

(C )

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MCQ 21 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

Correct option: A.

$\tan \frac{\alpha}{2}+\tan \frac{\beta}{2}+\tan \frac{r}{2}=\tan \frac{\alpha}{2} \tan \frac{\beta}{2} \tan \frac{r}{2}$

(A)

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MCQ 31 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

Correct option: D.

$\frac{1}{\sqrt{2}}$

(D)

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MCQ 41 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

Correct option: C.

$4 \cos ^3 A-3 \cos A$

(C )

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MCQ 51 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

Correct option: A.

$3 \sin A-4 \sin ^3 A$

(A)

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MCQ 61 Mark

$\cos \left(45^{\circ}-A\right) \cos \left(45^{\circ}-B\right)-\sin \left(45^{\circ}-A\right) \sin \left(45^{\circ}-B\right)$ is equal to :

✓
$\sin (A+B)$
B
$\sin (A-B)$
C
$\cos ( A + B )$
D
$\cos ( A - B )$

Answer

Correct option: A.

$\sin (A+B)$

(A)

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MCQ 71 Mark

The value of $\cos ^2\left(\frac{\pi}{8}+\frac{x}{2}\right)-\sin ^2\left(\frac{\pi}{8}-\frac{x}{2}\right)$ is :

A
$\sqrt{2} \cos x$
✓
$\frac{1}{\sqrt{2}} \cos x$
C
$2 \sin \frac{x}{2}$
D
$2 \cos \frac{x}{2}$

Answer

Correct option: B.

$\frac{1}{\sqrt{2}} \cos x$

(B)

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MCQ 81 Mark

The value of $\sin \left(60^{\circ}- A \right) \cos \left(30^{\circ}- B \right)+\cos \left(60^{\circ}\right.$ $- A ) \sin \left(30^{\circ}- B \right)$ is :

A
$\sin (A+B)$
B
$\sin (A-B)$
✓
$\cos ( A + B )$
D
$\cos (A-B)$

Answer

Correct option: C.

$\cos ( A + B )$

(C )

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MCQ 91 Mark

If $\tan ( A + B )=p$ and $\tan ( A - B )=q$, then the value of $\tan 2 A$ in terms of $p$ and $q$ is :

A
$\frac{p+q}{p-q}$
B
$\frac{p-q}{1+p q}$
✓
$\frac{p+q}{1-p q}$
D
$\frac{1+p q}{1-p}$

Answer

Correct option: C.

$\frac{p+q}{1-p q}$

(C )

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MCQ 101 Mark

If $\tan \alpha=\frac{5}{6}$ and $\tan \beta=\frac{1}{11}$, then the value of $\tan$ $(\alpha+\beta)$ is :

A
$\pi$
B
$\frac{\pi}{2}$
✓
$\frac{\pi}{4}$
D
$0$

Answer

Correct option: C.

$\frac{\pi}{4}$

(C )

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MCQ 111 Mark

If $\sin ^2 \theta=3 \cos ^2 \theta$, then the value of $\theta$ is :

✓
$60^{\circ}, 120^{\circ}, 240^{\circ}, 300^{\circ}$
B
$60^{\circ}, 120^{\circ}, 240^{\circ}, 315^{\circ}$
C
$60^{\circ}, 150^{\circ}, 240^{\circ}, 300^{\circ}$
D
$60^{\circ}, 120^{\circ}, 210^{\circ}, 315^{\circ}$

Answer

Correct option: A.

$60^{\circ}, 120^{\circ}, 240^{\circ}, 300^{\circ}$

(A)

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MCQ 121 Mark

If $A + B + C =\frac{\pi}{2}$, then the value of $\sin ( A + B )$ is :

A
$\sin C$
✓
$\cos C$
C
$-\sin C$
D
$-\cos C$

Answer

Correct option: B.

$\cos C$

(B)

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MCQ 131 Mark

$2 \sin A \sin B$ is equal to :

A
$\sin (A+B)+\sin (A-B)$
B
$\sin (A+B)-\sin (A-B)$
C
$\cos ( A + B )+\cos ( A - B )$
✓
$\cos (A-B)-\cos (A+B)$

Answer

Correct option: D.

$\cos (A-B)-\cos (A+B)$

(D)

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MCQ 141 Mark

$2 \cos A \cos B$ is equal to:

A
$\cos ( A + B )-\cos ( A - B )$
✓
$\cos ( A + B )+\cos ( A - B )$
C
$\cos (A-B)-\cos (A+B)$
D
None of the above

Answer

Correct option: B.

$\cos ( A + B )+\cos ( A - B )$

(B)

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MCQ 151 Mark

The position of the revolving line in tracing an angle of $550^{\circ}$ will be :

A
In first quadrant
B
In second quadrant
✓
In third quadrant
D
In fourth quadrant

Answer

Correct option: C.

In third quadrant

(C )

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MCQ 161 Mark

The value of $\cos \left(-660^{\circ}\right)$ is :

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

Answer

Correct option: C.

$\frac{1}{2}$

(C )

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MCQ 171 Mark

If $A+B+C=90^{\circ}$, then the value of $\tan (B+C)$ is :

A
$\tan A$
B
$-\tan A$
✓
$\cot A$
D
$-\cot A$

Answer

Correct option: C.

$\cot A$

(C )

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MCQ 181 Mark

The value of $\cos 960^{\circ}$ is :

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

Answer

Correct option: A.

$\frac{1}{2}$

(A)

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MCQ 191 Mark

The value of $\tan 3 A-\tan 2 A-\tan A$ is :

✓
$\tan 3 A \tan 2 A \tan A$
B
$-\tan 3 A \tan 2 A \tan A$
C
$\tan A \tan 2 A-\tan 2 A \tan 3 A-\tan 3 A \tan A$
D
$0$

Answer

Correct option: A.

$\tan 3 A \tan 2 A \tan A$

(A)

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MCQ 201 Mark

If $A + B + C =\pi$, then the value of $\tan \left(\frac{ A + B }{2}\right)$ is :

A
$\tan C$
B
$\tan \frac{C}{2}$
✓
$\cot \frac{ C }{2}$
D
$-\cot C$

Answer

Correct option: C.

$\cot \frac{ C }{2}$

(C )

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MCQ 211 Mark

If $\frac{\sin (x+y)}{\sin (x-y)}=\frac{a+b}{a-b}$, then the value of $\frac{\tan x}{\tan y}$ is :

✓
$\frac{a}{b}$
B
$\frac{b}{a}$
C
$\frac{a^2}{b^2}$
D
$a \cdot b$

Answer

Correct option: A.

$\frac{a}{b}$

(A)

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MCQ 221 Mark

If $\sin \alpha+\sin \beta=a$ and $\cos \alpha+\cos \beta=b$ then the value of $\cos (\alpha-\beta)$ is :

✓
$\frac{1}{2}\left(a^2+b^2-2\right)$
B
$\frac{1}{2}\left(a^2+b^2+2\right)$
C
$\frac{1}{2}\left(a^2-b^2-2\right)$
D
$\frac{1}{2}\left(-a^2+b^2+2\right)$

Answer

Correct option: A.

$\frac{1}{2}\left(a^2+b^2-2\right)$

(A)

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MCQ 231 Mark

If $\sin A=\frac{3}{5}$ and $\cos B=\frac{9}{41}$ and $A$ and $B$ are acute angles, then the value of $\cos ( A + B )$ :

A
$-\frac{133}{205}$
✓
$-\frac{84}{205}$
C
$\frac{84}{205}$
D
$\frac{133}{205}$

Answer

Correct option: B.

$-\frac{84}{205}$

(B)

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Maths M.C.Q (1 Marks)

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