Trigonometric Ratios & Identities · Mathematics · COMEDK

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MCQ (Single Correct Answer)

1
The value of $\frac{\sin ^2 20^{\circ}+\cos ^4 20^{\circ}}{\sin ^4 20^{\circ}+\cos ^2 20^{\circ}}$ is :
COMEDK 2025 Evening Shift
2
If $\tan \alpha=\frac{1}{7}$ and $\sin \beta=\frac{1}{\sqrt{10}}, \quad 0<\alpha, \beta<\frac{\pi}{2}$ then $2 \beta$ is equal to
COMEDK 2025 Evening Shift
3
If $\cos A=\frac{3}{4}$, then $\left(32 \sin \frac{A}{2} \sin \frac{5 A}{2}\right)=$
COMEDK 2025 Afternoon Shift
4

Simplified expression of

$1-\frac{\sin ^2 y}{1+\cos y}+\frac{1+\cos y}{\sin y}-\frac{\sin y}{1-\cos y}$ is :

COMEDK 2025 Afternoon Shift
5
If $\sin A+\sin B=-\frac{21}{65}, \cos A+\cos B=-\frac{27}{65}$ and $\pi
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6
The value of $\frac{1}{2 \sin 10^{\circ}}-2 \sin 70^{\circ}$ is
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7
If $\tan x^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \ldots \ldots \ldots . . \tan 88^{\circ} \tan y^{\circ}=1$ then $\cot (x+y)=$
COMEDK 2025 Morning Shift
8

$$ \text { If } \frac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y= $$

COMEDK 2024 Evening Shift
9

$$ \sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}} \text { where } \theta \in\left[-\frac{\pi}{8}, \frac{\pi}{8}\right] \text { is equal to } $$

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10

$$ \text { Value of } \cos 105^{\circ} \text { is } $$

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11

$$ \text { If } \frac{x}{\cos \theta}=\frac{y}{\cos \left(\theta+\frac{2 \pi}{3}\right)}=\frac{z}{\cos \left(\theta-\frac{2 \pi}{3}\right)} \text { then } x+y+z \text { is equal to } $$

COMEDK 2024 Afternoon Shift
12

$$ \frac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}= $$

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13

$$ \left(\cos \frac{\pi}{12}-\sin \frac{\pi}{12}\right)\left(\tan \frac{\pi}{12}+\cot \frac{\pi}{12}\right)= $$

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14

If $$\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$$ then $$\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=$$

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15

$$4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right) \text { is equal to }$$

COMEDK 2024 Morning Shift
16

$$ \text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in first and third quadrant respectively. Then } \cos (A+B)= $$

COMEDK 2024 Morning Shift
17

If $$\cos A=m \cos B$$ and $$\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$$, then $$\lambda$$ is equal to

COMEDK 2023 Morning Shift
18

The expression $$\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}$$ can be written as

COMEDK 2023 Morning Shift
19

$$ \cos ^6 A-\sin ^6 A \text { is equal to } $$

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20

$$ \text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is } $$

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21

If $$\cos \alpha=k \cos \beta$$ then $$\cot \left(\frac{\alpha+\beta}{2}\right)$$ is equal to

COMEDK 2023 Evening Shift
22

If $$\sin A+\sin B=a$$ and $$\cos A+\cos B=b$$, then $$\cos (A+B)$$ equals?

COMEDK 2022
23

What is $${{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}$$ equal to?

COMEDK 2022
24

If x and y are acute angles, such that $$\cos x + \cos y = {3 \over 2}$$ and $$\sin x + \sin y = {3 \over 4}$$, then $$\sin (x + y)$$ equals

COMEDK 2021
25

The expression $${{\tan A} \over {1 - \cot A}} + {{\cot A} \over {1 - \tan A}}$$ can be written as

COMEDK 2021
26

$${\sin ^2}17.5^\circ + \sin 72.5^\circ $$ is equal to

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