Which one of the following is possible?

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(C) The range of $\sin 	heta$ and $\cos 	heta$ is $[-1, 1]$. The range of $\sec 	heta$ is $(-\infty, -1] \cup [1, \infty)$. The range of $	an 	he

Vedclass · Accepted Answer

$	an 	heta = 45$

Vedclass · Answer

(C) The range of $\sin 	heta$ and $\cos 	heta$ is $[-1, 1]$. The range of $\sec 	heta$ is $(-\infty, -1] \cup [1, \infty)$. The range of $	an 	heta$ is $(-\infty, \infty)$.$(a)$ For $\sin 	heta = \frac{a^{2}+b^{2}}{a^{2}-b^{2}}$,if we take $a=2, b=1$,then $\sin 	heta = \frac{5}{3} > 1$,which is impossible.$(b)$ For $\sec 	heta = \frac{4}{5} = 0.8$,which is impossible since $|sec 	heta| \geq 1$.$(c)$ For $	an 	heta = 45$,this is possible as the range of $	an 	heta$ is all real numbers.$(d)$ For $\cos 	heta = \frac{7}{3} > 1$,which is impossible.Therefore,option $(c)$ is correct.

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