Which of the following equations has no solut | vedclass

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(B) The range of the trigonometric functions are as follows:$1$. For $\sin 	heta$ and $\cos 	heta$,the value must lie in the interval $[-1, 1]$.$2$.

Vedclass · Accepted Answer

$\cos 	heta = \sqrt{2}$

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(B) The range of the trigonometric functions are as follows:$1$. For $\sin 	heta$ and $\cos 	heta$,the value must lie in the interval $[-1, 1]$.$2$. For $\sec 	heta$ and $\csc 	heta$,the value must lie in $(-\infty, -1] \cup [1, \infty)$.$3$. For $	an 	heta$ and $\cot 	heta$,the value can be any real number $(R)$.Evaluating the options:- Option $A$: $\sec 	heta = 23$ is possible since $23 \in (-\infty, -1] \cup [1, \infty)$.- Option $B$: $\cos 	heta = \sqrt{2} \approx 1.414$. Since $1.414 > 1$,this value lies outside the range $[-1, 1]$. Thus,$\cos 	heta = \sqrt{2}$ has no solution.- Option $C$: $	an 	heta = 2019$ is possible since the range of $	an 	heta$ is $R$.- Option $D$: $\sin 	heta = -\frac{1}{5} = -0.2$ is possible since $-0.2 \in [-1, 1]$.Therefore,the correct option is $B$.

Which of the following equations has no solution?

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