1
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

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

A
$$\left(\frac{1}{8}, \frac{3}{8}, \frac{1}{2}\right)$$
B
$$\left(\frac{1}{8}, \frac{1}{2}, \frac{3}{8}\right)$$
C
$$\left(\frac{1}{2}, \frac{1}{8}, \frac{3}{8}\right)$$
D
$$\left(\frac{1}{2}, \frac{3}{8}, \frac{1}{8}\right)$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

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

A
$$\cos 2 \theta$$
B
$$\cot 2 \theta$$
C
$$\tan 2 \theta$$
D
$$\operatorname{cosec} \theta+\sin \theta$$
3
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

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

A
0
B
32
C
23
D
2
4
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

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

A
$$\cos \theta-\sin \theta$$
B
$$\sin \theta-\cos \theta$$
C
$$\cos \theta+\sin \theta$$
D
$$(1-\tan \theta) \sin \theta$$
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