A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
tan^2x + sec^2x=1
anonymous
 one year ago
tan^2x + sec^2x=1

This Question is Closed

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you need to prove this identity?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Rewrite tan x and sec x in terms of sin x and cos x. Then multiply both sides by \(\cos^2 x\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1yes. what about tan? what is tan in terms of sin and cos?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437335013169:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437335106407:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Right. tan x = sin x / cos x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\tan^2x + \sec^2x=1\) \(\dfrac{\sin^2x}{\cos^2 x} + \dfrac{1}{\cos^2x}=1\) Now multiply both sides by \(\cos^2 x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sin^2x/cos^2x=cos^2x?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\dfrac{\sin^2x}{\cos^2 x} + \dfrac{1}{\cos^2x}=1\) Now we multiply both sides by \(\cos ^2 x\) \( \cos^2 x(\dfrac{\sin^2x}{\cos^2 x} + \dfrac{1}{\cos^2x})=1 \times \cos^2 x\) \( \dfrac{\sin^2x \cancel{\cos^2 x}}{\cancel{\cos^2 x}~~1} + \dfrac{\cancel{\cos^2 x}~~1}{\cancel{\cos^2x}~~1})= \cos^2 x\) \( \sin^2 x + 1 = \cos^2 x\) \(1 = \sin^2 x + \cos^2 x\) \(\sin^2 x + \cos^2 x = 1\) The last equation is a wellknown trig identity.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you >.< ill work harder to memorize the identities
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.