A community for students.
Here's the question you clicked on:
 0 viewing
Directrix
 4 years ago
If x and y are acute angles whose sum is 60 degrees, what is the largest possible value of the following: (tan x)(tan y)?
Directrix
 4 years ago
If x and y are acute angles whose sum is 60 degrees, what is the largest possible value of the following: (tan x)(tan y)?

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Are you upto solving this set: http://answers.yahoo.com/question/index?qid=20111214061522AA8yZ07 ?

Directrix
 4 years ago
Best ResponseYou've already chosen the best response.2No. But, it appears that some yahoo may be guilty of _____. I wish I could see the date the question was posed.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Um just guessing, is \( \large \frac13 \) is the answer?

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.1yes it is:) i'm working on proving it though, taking derivative didn't get me anywhere

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Aha, I just used inequalities, the simple AMGM one, in more simple terms the for constant sum the product of two variables is highest when they are equal.

Directrix
 4 years ago
Best ResponseYou've already chosen the best response.2Yes, 1/3 is correct and can be concluded intuitively. The proof is not too bad.

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.1i know im over complicating it, but here is a proof using trig tan(x+y) = tan(60) = sqrt3 \[\tan(x+y) = \frac{\tan x +\tan y}{1\tan x \tan y}\] \[\rightarrow \frac{\tan x +\tan y}{1\tan x \tan y} = \sqrt{3}\] solving for (tanx)(tany) \[\tan x \tan y = 1 \frac{\tan x +\tan y}{\sqrt{3}}\] Differentiating: \[\rightarrow  \frac{\sec^{2} x +y'\sec^{2} y}{\sqrt{3}}\] Now y = 60x, so y' = 1 setting derivative equal to 0 \[ \frac{\sec^{2} y \sec^{2} x}{\sqrt{3}} = 0 \rightarrow \sec^{2}y = \sec^{2}x\] \[\rightarrow y=x\] Thus proving (tanx)(tany) is maximized when x=y=30 \[\tan 30 *\tan 30 = \frac{1}{3}\]
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.