First slide

Extreme values of trigonometric functions in trigonometry

Question

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

Moderate

A

4
B

3
C

5
D

6

Solution

Using A.M. $\geq$ G.M.
$\frac{\sin θ + \sin θ + \sin θ + {cosec}^{3} θ}{4} \geq {(\sin^{3} θ \cdot {cosec}^{3} θ)}^{1 / 4}$
Hence, minimum value of $3 \sin θ + {cosec}^{3} θ is 4$

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