Question

Verify that the equation is an identity. secºx- tan x=2 sec?x-1 To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the e each step Factor the ecºx - tanx= (sec?x+tan tan) two squares. sec difference of (Тут sec?x-2 sec x tan x + tan x sec?x+2 sec x tanx + tanx sec?x + tanx secx-tan? Choose an identity, ar 2. ary ans

Answer 1

$\text{Answer:} \\ \\ \sec^4(x)-\tan^4(x) =\fbox{\left(\sec^2(x)-\tan^2(x)\right)}\left(\sec^2(x)+\tan^2(x)\right) \\ ~~~~~~~~~~~~~~~~~~~~~~~= \fbox{1}\left(\sec^2(x)+\tan^2(x)\right)~\fbox{\text{Apply Pythagorean identity}} \\ \\ =\sec^2(x)+\tan^2(x)=\sec^2(x)+\sec^2(x)-1=2\sec^2(x)-1$

[ as x = (se Secun-tan" x = See'x-tan'a (se See²x+ tant x) as a-6 = (a - b) (a+b] See" a-tana see-x)?-(tan'd)? (se See?x-tana identity (see See²x + tana Apply Pythagorean See² x-tana = 1 - seen (sex - 1) tan x= see x-l see x + tanx 1 et = 2 Sec?x-1 Proof: See²a-taña Sina Cosa Cosa 1-sina Costa = Coo a = 1 Cosa CS Scanned with CamScanner