Which of the following statements is/are corr | vedclass

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(A, C) For $0 < 	heta < \frac{\pi}{2}$,the function $f(x) = \cos x$ is monotonically decreasing. We use the property that for $0 < \alpha < \beta < \

Vedclass · Accepted Answer

$\cos \frac{5	heta}{6} \geq (\cos 	heta)^{5/6}$

Vedclass · Answer

(A, C) For $0 We use the property that for $0  \cos \beta$. Also,for $0  (\cos 	heta)^q$. $(a)$ Since $\frac{	heta}{2}  \cos 	heta$. Raising to power $1/2$,$(\cos 	heta)^{1/2} \leq \cos \frac{	heta}{2}$ is correct. $(b)$ Since $\frac{3	heta}{4}  \cos 	heta$. Thus $(\cos 	heta)^{3/4} $(c)$ Since $\frac{5	heta}{6}  \cos 	heta$. Thus $\cos \frac{5	heta}{6} > (\cos 	heta)^{5/6}$. The statement is correct. $(d)$ Since $\frac{7	heta}{8}  \cos 	heta$. Thus $\cos \frac{7	heta}{8} > (\cos 	heta)^{7/8}$. The statement is incorrect.

Which of the following statements is/are correct for $0 < \theta < \frac{\pi}{2}$?

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