A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
verify cos(x)/(1+sin(x))+(1+sin(x))/cos(x)=2sec(x)
anonymous
 one year ago
verify cos(x)/(1+sin(x))+(1+sin(x))/cos(x)=2sec(x)

This Question is Closed

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437698487751:dw

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2manipulate the left side \[\frac{\cos \left(x\right)}{1+\sin \left(x\right)}+\frac{1+\sin \left(x\right)}{\cos \left(x\right)}\] \[\mathrm{Simplify}\:\frac{1+\sin \left(x\right)}{\cos \left(x\right)}+\frac{\cos \left(x\right)}{1+\sin \left(x\right)}:\quad \frac{\left(\sin \left(x\right)+1\right)^2+\cos ^2\left(x\right)}{\cos \left(x\right)\left(\sin \left(x\right)+1\right)}\] \[=\frac{\left(1+\sin \left(x\right)\right)^2+\cos ^2\left(x\right)}{\left(1+\sin \left(x\right)\right)\cos \left(x\right)}\] \[\mathrm{Use\:the\:following\:identity}:\quad \cos ^2\left(x\right)=1\sin ^2\left(x\right)\] \[=\frac{\left(1+\sin \left(x\right)\right)^2+1\sin ^2\left(x\right)}{\left(1+\sin \left(x\right)\right)\cos \left(x\right)}\] \[\mathrm{Simplify}\:\frac{\left(1+\sin \left(x\right)\right)^2+1\sin ^2\left(x\right)}{\left(1+\sin \left(x\right)\right)\cos \left(x\right)}:\quad \frac{2}{\cos \left(x\right)}\] \[\mathrm{Use\:the\:following\:identity:}\:\cos \left(x\right)=\frac{1}{\sec \left(x\right)}\] \[=\frac{2}{\frac{1}{\sec \left(x\right)}}\] \[=2\sec \left(x\right)\]

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2are you understand @tamez1210
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.