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Question
`lim_(x -> pi/4) (sec^2x - 2)/(tan x - 1)` is equal to ______.
Options
3
1
0
2
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Solution
`lim_(x -> pi/4) (sec^2x - 2)/(tan x - 1)` is equal to 2.
Explanation:
Given, `lim_(x -> pi/4) (sec^2 x - 2)/(tan x - 1)`
= `lim_(x -> pi/4) (1 + tan^2 x - 2)/(tan x - 1)`
= `lim_(x -> pi/4) (tan^2x - 1)/(tanx - 1)`
= `lim_(x -> pi/4) ((tan x + 1)(tan x - 1))/((tan x - 1))`
= `lim_(x -> pi/4) (tan x + 1)`
= `tan pi/4 + 1`
= 1 + 1
= 2
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