Very interesting problem

Prove tan{(3pi)/11} + 4tan{(2pi)/11} =110.511^{0.5}= square root of 11...

Note by Kiran Patel
7 years, 11 months ago

No vote yet
3 votes

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

The problem actually is as follows, and I request the user to edit it. Iam not giving the solution, and that googling it will give the solution:

Prove that tan3π11+4sin2π11tan \frac {3\pi}{11} + 4sin \frac {2\pi}{11}= 11\sqrt 11

Infact, even the following relations hold:

tan3π11+4sin2π11tan \frac {3\pi}{11} + 4sin \frac {2\pi}{11}= 11\sqrt 11

tan4π11+4sinπ11tan \frac {4\pi}{11} + 4sin \frac {\pi}{11}= 11\sqrt 11

tan5π114sin4π11tan \frac {5\pi}{11} - 4sin \frac {4\pi}{11}= 11\sqrt 11

tan2π114sin5π11tan \frac {2\pi}{11} - 4sin \frac {5\pi}{11}= 11-\sqrt 11

tanπ11+4sin3π11tan \frac {\pi}{11} + 4sin \frac {3\pi}{11}= 11\sqrt 11

Shourya Pandey - 7 years, 11 months ago

Log in to reply

By the way, you should put braces around your eleven's that are under the square root, so that the entire radican is covered by the bar of the square root. It should look like \sqrt{11} rather than \sqrt11, so that 11\sqrt{11}, rather than 11\sqrt11, appears. :)

Bob Krueger - 7 years, 11 months ago

Are you sure this is what we have to prove? Because I just used a calculator and saw that tan(3π11)+4tan(2π11)tan(\frac{3\pi}{11}) +4tan(\frac{2\pi}{11}) is not equal to the square root of 1111. Am I somehow misunderstanding your problem?

Mursalin Habib - 7 years, 11 months ago

But in my book its tan and not sine....but yes it must be sine.....

Kiran Patel - 7 years, 11 months ago

Log in to reply

maybe some mistake

Shourya Pandey - 7 years, 11 months ago
×

Problem Loading...

Note Loading...

Set Loading...