Find the limit of (1-tan(1)x)/(cos(2)x) as x approaches pi/2

 Exercise

$\lim_{x\to\frac{\pi}{2}}\left(\frac{1-\tan\left(1\right)\left(x\right)}{\cos\left(2\right)x}\right)$

 Step-by-step Solution

 

Evaluate the limit $\lim_{x\to{\frac{\pi }{2}}}\left(\frac{1-\tan\left(1\right)x}{\cos\left(2\right)x}\right)$ by replacing all occurrences of $x$ by $\frac{\pi }{2}$

$\frac{1-\tan\left(1\right)\cdot \left(\frac{\pi }{2}\right)}{\cos\left(2\right)\cdot \frac{\pi }{2}}$

 

Multiply the fraction and term in $-\tan\left(1\right)\cdot \left(\frac{\pi }{2}\right)$

$\frac{1-\frac{\pi }{2}\tan\left(1\right)}{\cos\left(2\right)\cdot \frac{\pi }{2}}$

Final answer to the exercise  

$\frac{1-\frac{\pi }{2}\tan\left(1\right)}{\cos\left(2\right)\cdot \frac{\pi }{2}}$

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 Exercise

 Step-by-step Solution

 Final answer to the exercise  

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Final answer to the exercise  