Trigonometric Ratios & Identities · Mathematics · AP EAPCET

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MCQ (Single Correct Answer)

1
If $A, B, C$ are the angles of triangle, then $\sin 2 A-\sin 2 B+\sin 2 C=$
AP EAPCET 2024 - 21th May Evening Shift
2

Assertion (A) : If $A=10^{\circ}, B=16^{\circ}$ and $C=19^{\circ}$, then $\tan 2 A \tan 2 B+\tan 2 B \tan 2 C+\tan 2 C \tan 2 A=1$

Reason (R) : If $A+B+C=180^{\circ}, \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}$

$$ =\cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} $$

Which of the following is correct ?

AP EAPCET 2024 - 21th May Evening Shift
3
If $\alpha$ is in the 3rd quadrant, $\beta$ is in the 2nd quadrant such that $\tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}$, then $\sin (2 \alpha+\beta)=$
AP EAPCET 2024 - 21th May Evening Shift
4
If the period of the function $f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}$ is $\alpha$, then $f\left(\frac{\alpha}{8}\right)=$
AP EAPCET 2024 - 21th May Morning Shift
5
If $\sin x+\sin y=\alpha, \cos x+\cos y+\beta$, then $\operatorname{cosec}(x+y)=$
AP EAPCET 2024 - 21th May Morning Shift
6
If $P+Q+P=\frac{\pi}{4}$, then $\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos$ $\left(\frac{\pi}{8}-R\right)=$
AP EAPCET 2024 - 21th May Morning Shift
7
If $\theta$ is an acute angle, $\cosh x=K$ and $\sinh x=\tan \theta$, then $\sin \theta=$
AP EAPCET 2024 - 21th May Morning Shift
8
If $\sec \theta+\tan \theta=\frac{1}{3}$, then the quadrant in which $2 \theta$ lies is
AP EAPCET 2024 - 20th May Evening Shift
9
If $540^{\circ} < A < 630^{\circ}$ and $|\cos A|=\frac{5}{13}$, then $\tan \frac{A}{2} \tan A=$
AP EAPCET 2024 - 20th May Evening Shift
10
If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$
AP EAPCET 2024 - 20th May Evening Shift
11
If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then $\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=$
AP EAPCET 2024 - 20th May Morning Shift
12
$$ \text { } \frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}= $$
AP EAPCET 2024 - 20th May Morning Shift
13
$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots . . .+\sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1}=$
AP EAPCET 2024 - 20th May Morning Shift
14
The value of $5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between
AP EAPCET 2024 - 19th May Evening Shift
15

Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$

Statement (S2) Range of $\frac{1}{3-\cos 2 x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$

Which one of the following is correct?

AP EAPCET 2024 - 19th May Evening Shift
16
$ \tan 6^\circ + \tan 42^\circ + \tan 66^\circ + \tan 78^\circ = $
AP EAPCET 2024 - 18th May Morning Shift
17
The maximum value of $12\sin x - 5\cos x + 3$ is
AP EAPCET 2024 - 18th May Morning Shift
18
$\sin^2 16^\circ - \sin^2 76^\circ = $
AP EAPCET 2024 - 18th May Morning Shift
19
By considering $1^{\prime}=0.0175$, he approximate value of $\cot 45^{\circ} 2^{\prime}$ is
AP EAPCET 2024 - 18th May Morning Shift
20

If $$\sin ^4 \theta \cos ^2 \theta=\sum_\limits{n=0}^{\infty} a_{2 n} \cos 2 n \theta$$, then the least $$n$$ for which $$a_{2 n}=0$$ is

AP EAPCET 2022 - 5th July Morning Shift
21

If $$\sin \theta=-\frac{3}{4}$$, then $$\sin 2 \theta=$$

AP EAPCET 2022 - 5th July Morning Shift
22

$$\begin{aligned} & \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\ldots +\frac{1}{\sin 89^{\circ}+\sin 90^{\circ}}= \end{aligned}$$

AP EAPCET 2022 - 5th July Morning Shift
23

Which of the following trigonometric values are negative?

I. $$\sin \left(-292^{\circ}\right)$$

II. $$\tan \left(-190^{\circ}\right)$$

III. $$\cos \left(-207^{\circ}\right)$$

IV. $$\cot \left(-222^{\circ}\right)$$

AP EAPCET 2022 - 5th July Morning Shift
24

$$\sin ^2 \frac{2 \pi}{3}+\cos ^2 \frac{5 \pi}{6}-\tan ^2 \frac{3 \pi}{4}=$$

AP EAPCET 2022 - 5th July Morning Shift
25

A true statement among the following identities is

AP EAPCET 2022 - 4th July Evening Shift
26

If $$A+B+C=\pi, \cos B=\cos A \cos C$$, then $$\tan A \tan C=$$

AP EAPCET 2022 - 4th July Evening Shift
27

The value of $$\tan \left(\frac{7 \pi}{8}\right)$$ is

AP EAPCET 2022 - 4th July Evening Shift
28

$$1+\sec ^2 x \sin ^2 x=$$

AP EAPCET 2022 - 4th July Evening Shift
29

If the identity $$\cos ^4 \theta=a \cos 4 \theta+b \cos 2 \theta+c$$ holds for some $$a, b, c \in Q$$ then $$(a, b, c)=$$

AP EAPCET 2022 - 4th July Morning Shift
30

The value of $$\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}$$ is

AP EAPCET 2022 - 4th July Morning Shift
31

If $$(1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,$$ then $$n=$$

AP EAPCET 2022 - 4th July Morning Shift
32

$$\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=$$

AP EAPCET 2022 - 4th July Morning Shift
33

If $$\operatorname{cosech} x=\frac{4}{5}$$, then $$\sinh x=$$

AP EAPCET 2022 - 4th July Morning Shift
34

What is the value of $$\cos \left(22 \frac{1}{2}\right)^{\circ}$$ ?

AP EAPCET 2021 - 20th August Morning Shift
35

If $$\cos \theta=-\sqrt{\frac{3}{2}}$$ and $$\sin \alpha=\frac{-3}{5}$$, where '$$\theta$$' does not lie in the third quadrant, then the value of $$\frac{2 \tan \alpha+\sqrt{3} \tan \theta}{\cot ^2 \theta+\cos \alpha}$$ is equal to

AP EAPCET 2021 - 20th August Morning Shift
36

If $$\tan \beta=\frac{\tan \alpha+\tan \gamma}{1+\tan \alpha \tan \gamma}$$, then $$\frac{\sin 2 \alpha+\sin 2 \gamma}{1+\sin 2 \alpha \sin 2 \gamma}$$ is equal to

AP EAPCET 2021 - 20th August Morning Shift
37

The sides of a triangle inscribed in a given circle subtend angles $$\alpha, \beta, \gamma$$ at the center. The minimum value of the AM of $$\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)$$ and $$\cos \left(\gamma+\frac{\pi}{2}\right)$$ is equal to

AP EAPCET 2021 - 20th August Morning Shift
38

In a $$\triangle A B C$$, if $$3 \sin A+4 \cos B=6$$ and $$4 \sin B+3 \cos A=1$$, then $$\sin (A+B)$$ is equal to

AP EAPCET 2021 - 19th August Evening Shift
39

$$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$$ is equal to

AP EAPCET 2021 - 19th August Evening Shift
40

If $$f(x)=\frac{\cot x}{1+\cot x}$$ and $$\alpha+\beta=\frac{5 \pi}{4}$$, then the value of $$f(\alpha) f(\beta)$$ is equal to

AP EAPCET 2021 - 19th August Evening Shift
41

In $$\triangle A B C \cdot \frac{a+b+c}{B C+A B}+\frac{a+b+c}{A C+A B}=3$$, then $$\tan \frac{C}{8}$$ is equal to

AP EAPCET 2021 - 19th August Evening Shift
42

Mean of the values $$\sin ^2 10 Y, \sin ^2 20 Y, \sin ^2 30 Y, \ldots \ldots \ldots ., \sin ^2 90 Y$$ is

AP EAPCET 2021 - 19th August Evening Shift
43

When the coordinate axes are rotated through an angle 135$$\Upsilon$$, the coordinates of a point $$P$$ in the new system are known to be $$(4,-3)$$. Then find the coordinates of $$P$$ in the original system.

AP EAPCET 2021 - 19th August Evening Shift
44

The maximum value of $$f(x)=\sin (x)$$ in the interval $$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$$ is

AP EAPCET 2021 - 19th August Evening Shift
45

$$\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
46

If $$\sin \alpha - \cos \alpha = m$$ and $$\sin 2\alpha = n - {m^2}$$, where $$ - \sqrt 2 \le m \le \sqrt 2 $$, then n is equal to

AP EAPCET 2021 - 19th August Morning Shift
47

If $$\sinh u=\tan \theta$$, then $$\cosh u$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
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