Explained: "Find the limit. limx→(π/2)sec⁡xtan⁡x"

Globokim8

Answered question

2021-01-27

Find the limit.

lim_{x \to (π / 2)} \frac{\sec x}{\tan x}

SabadisO

Skilled2021-01-28Added 108 answers

We have to evaluate

lim_{x \to (π / 2)^{-}} \frac{\sec x}{\tan x}

We can see that if we put given limit then we get

\frac{\infty}{\infty}

form.
So, to remove this form, we will simplify the given expression and then we will put limit.
We know that

\sec x = \frac{1}{\cos x}

and

\tan x = \frac{\sin x}{\cos x}

Therefore,

lim_{x \to (π / 2)^{-}} \frac{\sec x}{\tan x} = lim_{x \to (π / 2)^{-}} \frac{\frac{1}{\cos x}}{\frac{\sin x}{\cos x}}

lim_{x \to π / 2} \frac{1}{\sin x}

= \frac{1}{\sin \frac{π}{2}}

= \frac{1}{1}

= 1

Hence, required answer is 1 .

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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