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  • Choose the correct answer out of 4 options given against each Question lim┬(x→π/4) ((sec^2⁡x-2)/(tan⁡x-1)) is A. 3 B. 1 C. 0 D. root2

Choose the correct answer out of 4 options given against each Question

\mathop{\lim }_{x \rightarrow \frac{ \pi }{4}} \left( \frac{\sec ^{2}x-2}{\tan x-1} \right) is
A. 3
B. 1
C. 0
D. \sqrt{2}

Answers (1)

\\ \mathop{\lim }_{x \rightarrow \frac{ \pi }{4}} \left( \frac{\sec ^{2}x-2}{\tan x-1} \right)\\ =\mathop{\lim }_{x \rightarrow \frac{ \pi }{4}} \left( \frac{1+\tan ^{2}x-2}{\tan x-1} \right) \\=\mathop{\lim }_{x \rightarrow \frac{ \pi }{4}} \left( \frac{\tan ^{2}x-1}{\tan x-1} \right)\\ =\mathop{\lim }_{x \rightarrow \frac{ \pi }{4}} \left( \tan x+1 \right)\\ =2 \\ \\

Hence, the answer is option D

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