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  • <img alt="\mathrm{\text { If } f(x)=\frac{\sqrt{2} \cos x-1}{\cot x-1}, x \neq \pi / 4 \text { is continuous at } x=\pi / 4 \text {, then } f(\pi / 4) \text { is equal to }}" src="https://entrancec

\mathrm{\text { If } f(x)=\frac{\sqrt{2} \cos x-1}{\cot x-1}, x \neq \pi / 4 \text { is continuous at } x=\pi / 4 \text {, then } f(\pi / 4) \text { is equal to }}

Option: 1

1/2


Option: 2

\pi / 4


Option: 3

\pi / 2


Option: 4

\text { None of these }


Answers (1)

best_answer

\mathrm{ f\left(\frac{\pi}{4}\right)=\lim _{x \rightarrow \frac{\pi}{4}} \frac{\sqrt{2} \cos x-1}{\cot x-1}=\frac{\sqrt{2} \sin x}{\operatorname{cosec}^2 x}=\sqrt{2} \sin ^3 x=\frac{\sqrt{2}}{2 \sqrt{2}} \, \, }

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Rakesh

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