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1
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)$, then $f\left(\frac{\pi}{5}\right)=$

A
$\frac{3(\sqrt{5}-1)}{16}$
B
$\frac{3 \sqrt{10-2 \sqrt{5}}}{8}$
C
$\frac{3 \cdot \sqrt{10+2 \sqrt{5}}}{8}$
D
$\frac{3(\sqrt{5}+1)}{16}$
2
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
For $0 \leq x \leq \pi$, if $81^{\sin ^2 x}+81^{\cos ^2 x}=30$, then $x=$
A
$\frac{\pi}{6}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{15}$
D
$\frac{\pi}{8}$
3
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \frac{\left(1+\tan 32^{\circ}\right)}{\left(1-\tan 48^{\circ}\right)}= $$
A
1
B
2
C
3
D
4
4
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \sin \alpha+\cos \alpha=m \Rightarrow \sin ^6 \alpha+\cos ^6 \alpha= $$
A
$\frac{4+3\left(m^2-1\right)^2}{4}$
B
$\frac{4-3\left(m^2-1\right)^2}{4}$
C
$\frac{3+4\left(m^2-1\right)^2}{4}$
D
$\frac{4-3\left(m^2+1\right)^2}{4}$
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