A Quick Trigonometry Problem From the JEE Advanced Exam

[@randomjin9392]

You're getting away with the fact that among these solutions it's impossible to have cos(x) = 0 or sin(5x) = 0. Normally you would want to cover for the fact that both tangent and cotangent are defined in the original equation.

[@vcvartak7111]

I think the general solution should be pi/12+ pi/6(even integers) that will cater half solution s of pi/12+pi/3(integer)

[@霍金本人]

Wdym? pi/12+npi/3 is subset of pi/12+npi/6. And we are finding intersection of these two sets, so the sol is the subset which is pi/12+npi/3

[@georgekhy]

sin 2x = cos 4x = sin(pi/2 - 4x), so 2x = npi + (-1)^2 (pi/2 - 4x) Similar method works for tan and cot. It will be slightly more elementary.

[@george2358]

Another simpler way to solve this is by using the fact that tanx=cot(90-x) and sinx=cos(90-x)

[@mouskatoodle]

But this is only valid when x

[@rocky171986]

@@mouskatoodle It's valid over all real x, not just positive x

[@cobokobo2115]

@@mouskatoodle amazing .................kzbin.info/www/bejne/i52UepSlj8aahdE

[@mcwulf25]

More accurately, sin(X) = cos (2nπ+π/2 - X), which is the method I used.

[@mouskatoodle]

@@rocky171986 oh. I was not aware of that. Thank you for correcting me

[@STF413]

Why "some integers n" instead of "all integers n"?

[@adiaphoros6842]

“Some integer n” = “Where n is some integer” = “Where n is an arbitrary integer” = “For all integers n”

[@STF413]

@@adiaphoros6842 Actually, my question was rhetorical. "(For) some integer n" is *NOT* "For all integers n" because if something is true for a subset (cf "some integer n"), that does NOT mean the statement is true for the whole set. It was wrong to say "for some integer n"

[@adiaphoros6842]

@@STF413 TL;DR “For some integer” ≠ ”For some integers” The construction “for some [singular noun]” has been used in English to mean “for an arbitrary [singular noun]” Note, this is different from the construction “for some [plural noun]” If the latter is what you’re referring to, then you’re right. This is not a mathematical statement, rather a linguistic one. Though, I think he could’ve just written: ∀n∈ℤ which uses less characters.

[@STF413]

@@adiaphoros6842 LOL LOL LOL 🤣🤣🤣 Your argument is very flawed. Since you didn't want to read my comment (TL;DR), I don't see why I would explain more why you're wrong. Go ahead and think you're right if you like. There are a lot of "Dunning-Kruger"-ish people happily living in the world 😆

[@adiaphoros6842]

@@STF413 Are you talking about yourself? Since you’re arguing against something so obvious. Weird you tagged me.

[@QuentinStephens]

Why are you specifying integers rather than cardinals? Integers can be negative.

[@RGP_Maths]

Didn't you just answer your own question? The final solution is valid for all integers n, whether positive, negative or zero.

[@राजनगोंगल]

👏👏👏👏👏👏👍👍👍👍👍👍🙏🙏🙏🙏🙏🙏

[@swagmoneybuge]

Couldn't to rewrite cot(5x) to tan(1/5x) then do 1/5x=x and solve from there?

[@madhavrathi6770]

No , that's not how it works , I guess .

[@madhavrathi6770]

They are complementary so you could write that as cot(5x) = tan(90-5x)

[@STF413]

Of course not. Because cot (5x) = 1 / tan (5x) which is NOT tan (1/5x)

[@VaibhavRahalkar]

That rule apply for inverse functions

[@nirmankhan2134]

It could have been solved in a much more easier way

[@rishiraj5711]

Tell

[@tianqilong8366]

ez

[@數學系大大]

LOL