Solving A Non-Standard Trigonometric Equation

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[sin(3x)/sin(x)]-[cos(3x)/cos(x)]=x
#PolynomialEquations #Polynomials
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PLAYLISTS 🎵 :

[pseudoexpertise]

I was bored and expected something ugly. But the result is surprisingly beautiful!

[MortezaSabzian-dbsl]

Another method
We know;
Sin(x)=(e^(ix)-e^(-ix))/2i
And cos(x)=(e^(ix)+e^(-ix))/2
These results are obtained from Euler's
As result

I used this algebraic union to simplify
a³-b³=(a-b)(a²+b²+ab)
Similarly we have

The unknown value is determined by subtracting two relations from each other

[kevinmadden]

This question is found in many trigonometry textbooks, usually presented as an identity .

[MathsScienceandHinduism]

solved in seconds using 2nd method in my head.

[burlfromlondon]

You made a mistake in the cos triple angle formula but used the correct value in the calculation

[yoav]

Nice! X=2 is the solution for both videos in the main channel and the second channel, interesting..😃💯

[eduardocorrea]

Muy buena explicación. El segundo método es mucho más simple y más rápido. Saludos a todos.

[mywgueu]

Let x be π/4, then cot(π/4)-tan(π/4)=π/4

[YahiaNebti]

It's finding a numerical value for the left hand side more than an equation because you didn't touch the x term

[alextang]

sin(n*x) or cos(n*x) always turn into n degree equation. 😏😏😏😏😏😏

[ronm]

Hardest question ever: If x=2, then what is x?