# My Ist day on brilliant. & I am searching for friends.

$\\ Given\quad \sin { \theta } +\sin ^{ 2 }{ \theta } =1\\ find\quad \cos ^{ 12 }{ \theta } +3\cos ^{ 10 }{ \theta } +3\cos ^{ 8 }{ \theta } +\cos ^{ 6 }{ \theta } \quad -1\quad .$

This was my first question in brilliant ( excluding the question: next number in the sequence 2,4,8.. during account creation).

$Since\quad value\quad is\quad given\quad in\quad terms\quad of\quad sin\theta \quad I\quad thought\\ it\quad might\quad be\quad beneficial\quad to\quad convert\quad terms\quad of\quad cos\theta \quad in\quad \\ sin\theta \quad moreover\quad its\quad apparent\quad that\quad it\quad can\quad be\quad done\quad easily.\quad \\ After\quad substituting(\cos ^{ 2 }{ \theta } =\sin { \theta } )\quad I\quad got\quad these\quad terms:\\ \\ \sin ^{ 3 }{ \theta } +\sin ^{ 6 }{ \theta } +3\sin ^{ 4 }{ \theta } +3\sin ^{ 5 }{ \theta } -1\\ \\ Which\quad on\quad rearranging\quad gave\quad these:\\ \\ \Rightarrow \sin ^{ 3 }{ \theta } +\sin ^{ 6 }{ \theta } +3\sin ^{ 3 }{ \theta } (\sin ^{ 2 }{ \theta } +\sin { \theta } )-1\\ \\ I\quad finally\quad shot\quad the\quad problem\quad by\quad this:\\ \Rightarrow { (\sin { \theta } +\sin ^{ 2 }{ \theta } ) }^{ 3 }-1=0.\\ \\ I\quad used\quad to\quad face\quad (to\quad be\quad honest,I\quad still\quad face)\quad difficulty\quad while\quad \\ attempting\quad 'trigo'\quad problems.They\quad appear\quad to\quad me\quad so\quad absurd.\\ 'What\quad should\quad we\quad do\quad here?'\\ 'Why\quad would\quad anyone\quad do\quad that?'\\ 'OK!\quad good\quad solution\quad there\quad but\quad how\quad to\quad arrive\quad at\quad it?'\\ These\quad are\quad the\quad family\quad of\quad questions\quad clouding\quad over\quad my\\ mind.\quad So,\quad I\quad (honestly\quad try)\quad to\quad reason\quad out\quad my\quad steps.\\ \\ I\quad am\quad not\quad good\quad at\quad Mathematics.\quad But,\quad I\quad like\quad Maths.\quad \\ Here\quad in\quad brilliant.org,\quad there\quad are\quad very\quad talented\quad problem\quad solvers.\\ I\quad know\quad it\quad because\quad I\quad had\quad spent\quad some\quad time\quad with\quad my\quad friend,\quad \\ in\quad his\quad profile,\quad tackling\quad problems\quad and\quad viewing\\ solutions\quad and\quad reading\quad notes.\quad Then\quad it\quad allured\quad me\quad to\quad join\quad it.\\ \\ I\quad don't\quad have\quad collections\quad of\quad nut-cracking\quad problems\quad neither\quad \\ the\quad ability\quad to\quad shoot\quad those\quad type\quad of\quad questions\quad but\quad still\quad if\\ some\quad are\quad benefited\\ in\quad any\quad kind\quad through\quad me\quad \\ \\ I\quad would\quad be\quad glad.\\ \$/extract_itex] Note by Soumo Mukherjee 5 years, 5 months ago 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. numbered2. 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 1paragraph 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 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

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Wassup Math Philic!

I'm John - and I post the strangest problems around here ;)

I remember the first time I've discovered Brilliant. I Googled "very hard math problems," and clicked a link that led me here - and tell ya what, it's been one hella ride. Throughout the time being, I've discovered a community of intelligent and respectful individuals around the world who not only share math and physics problems and solutions but are willing to address your problems when you need it the most.

Let me introduce you to this site's Bomb Squad:

@Calvin Lin - The White Knight (if he reshares your problem, it's your lucky day!)

@Michael Mendrin - Mr. Mathopedia

@hasan kassim - King Integral

@Mardokay Mosazghi - coolest kid in town.

@jatin yadav - "can't" ain't in his dictionary.

@brian charlesworth - Dr. Philosophy

@Marios Patsios - don't mess with this one...

@David Mattingly - PHYSICS 101

@Peter Taylor - look at those mountains...

and

@Suyeon Khim - the one who started it all.

ss

There's many more, sorry if I forgot anyone, but trust me, there's WAY more...

Oh yeah...

And hey, don't be shy to try one of my most overrated problems about the Moon and the Universe: How to Climb to the Moon - it's a real teaser!

Oh, and we don't just have problems; we can discuss things all we want. Try out Physics Jokes!

Welcome to the club.

s

- 5 years, 5 months ago

Haha... "Dr. Philosophy" ... You're too funny. :) There were a couple of people on the "Bomb Squad" I wasn't familiar with, so thanks for making the list. I would add @Jon Haussmann as well as "The Annihilator" for the way he mows down countless difficult problems like they're nothin'.

@Math Philic Welcome! Just thought I'd offer a couple of pieces of advice:

• If you want more problems, notes, etc., to appear on your feed, just follow those you admire and then their posts and reshares will be placed on your feed.

• I notice that all your text is italicized. Most people find this a bit more difficult to read than standard font, so you may want to just use the LaTeX for the "math parts" of your posts. :)

- 5 years, 5 months ago

yes, for the use of latex part one of the moderator @Aditya Raut has helped me. Thanx to u 2 guys.I gonna follow the mentioned guys.. :)

- 5 years, 5 months ago

1 more thing.How to mention a name in comment?

- 5 years, 5 months ago

To mention a name, type the @ symbol followed by the name you wish to mention. Usually, as you're typing out the letters of the name there will be a drop-down list of names that match the letters typed to that point from which you can pick, (this option saves a bit of time). The person will be notified in their feed that they have been mentioned.

- 5 years, 5 months ago

Thanx @brian charlesworth

- 5 years, 5 months ago

U missed urself-the cool guy.. thanx mate for this intro..

- 5 years, 5 months ago