First slide

Means - A.M/G.M/H.M

Question

$If 0 < θ < π, then minimum value of 3 \sin θ + {cosec}^{3} θ is$

Moderate

A

4
B

5
C

6
D

3

Solution

$\begin{array}{l} Using Arithmetic mean (AM) \geq Geometric mean (GM) \\ \frac{\sin θ + \sin θ + \sin θ + {cosec}^{3} θ}{4} \geq {(\sin^{3} θ \cdot {cosec}^{3} θ)}^{\frac{1}{4}} \end{array}$
$\begin{array}{l} \Rightarrow 3 \sin θ + {cosec}^{3} θ \geq 4 \\ Hence, minimum value of 3 \sin θ + {cosec}^{3} θ is 4 \\ Therefore, the correct answer is (1) . \end{array}$

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