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1
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$\sin 2 A+\cos 2 A$$
B
$$2 \sec A \operatorname{cosec} A+2$$
C
$$\tan 2 A+\cot 2 A$$
D
$$\sec 2 A+\operatorname{cosec} 2 A$$
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ \cos 2 A\left(1-\frac{1}{4} \sin ^2 2 A\right) $$
B
$$ \cos 2 A\left(1-\frac{3}{4} \sin ^2 2 A\right) $$
C
$$ \cos 2 A\left(1-\frac{1}{2} \sin ^2 2 A\right) $$
D
$$ \cos 2 A\left(1+\frac{1}{4} \sin ^2 2 A\right) $$
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ \cot A $$
B
$$ \operatorname{cosec} A $$
C
$$ \tan A $$
D
$$ \sin A $$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ \frac{k+1}{k-1} \tan \left(\frac{\alpha-\beta}{2}\right) $$
B
$$ \frac{k+1}{k-1} \tan \left(\frac{\beta-\alpha}{2}\right) $$
C
$$ \frac{k-1}{k+1} \tan \left(\frac{\beta-\alpha}{2}\right) $$
D
$$ \frac{k-1}{k+1} \tan \left(\frac{\alpha-\beta}{2}\right) $$
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