Question

For $\theta \in (-\frac{\pi }{2},0)$, which of the following option are correct

• A. $\sin \theta <{\sin }^3\theta <{\cos }^2\theta$
• B. $\sin \theta <{\sin }^3\theta <\cos \theta$
• C. $\sin \theta <\cos \theta <\sec \theta$
• D. $Allofthese$

Answer 1

Answer: (C)

$\sin \theta <\cos \theta <\sec \theta$

For $\theta \in (-\frac{n}{2},0)$

$\cos \theta >0,\sin \theta <0,\sec \theta >0$

$\sec \theta >\cos \theta ($ as $\sec \theta =\frac{1}{\cos \theta }$ and $\cos \theta \in [-1,1])$

$\sin \theta <\cos \theta <\sec \theta$

option $C$ is correct.