+0

# how to evaluate the lim x-pi/4 (1-tan x)sec 2x?

0
1404
2

how to evaluate the lim x-pi/4 (1-tan x)sec 2x?

Guest May 26, 2015

#1
+26493
+15

$$(1-\tan x)\sec{2x} \rightarrow \frac{1-\tan x}{\cos{2x}} \rightarrow \frac{1-\tan x}{\cos^2{x}-\sin^2{x}}\rightarrow \frac{1-\tan x}{(1-\tan^2{x})\cos^2{x}}\\\\\rightarrow \frac{1-\tan x}{(1-\tan{x})(1+\tan{x})\cos^2{x}}\rightarrow \frac{1}{(1+\tan{x})\cos^2{x}}$$

tan(pi/4) = 1  and cos(pi/4) = 1/√2 so:

$$\frac{1}{(1+\tan{\frac{\pi}{4}})\cos^2{\frac{\pi}{4}}}=\frac{1}{2\times \frac{1}{2}}=1$$

.

Alan  May 26, 2015
Sort:

#1
+26493
+15

$$(1-\tan x)\sec{2x} \rightarrow \frac{1-\tan x}{\cos{2x}} \rightarrow \frac{1-\tan x}{\cos^2{x}-\sin^2{x}}\rightarrow \frac{1-\tan x}{(1-\tan^2{x})\cos^2{x}}\\\\\rightarrow \frac{1-\tan x}{(1-\tan{x})(1+\tan{x})\cos^2{x}}\rightarrow \frac{1}{(1+\tan{x})\cos^2{x}}$$

tan(pi/4) = 1  and cos(pi/4) = 1/√2 so:

$$\frac{1}{(1+\tan{\frac{\pi}{4}})\cos^2{\frac{\pi}{4}}}=\frac{1}{2\times \frac{1}{2}}=1$$

.

Alan  May 26, 2015
#2
+91797
+10

Thanks Alan,

I doubt I would have got that on my own EVEN if I had been a good enother forensic mathematician to work out the question in the first place.   LOL

I put this into the Great Answers to Learn from Sticky Thread :)

Melody  May 27, 2015

### 8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details