Math problems

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I have to solve these two equations but don't understand them at all. :S. Maybe you guys know how to do it?

sin (x-(1/4 * π) * cos x = (1/2*(2^0,5) ) * (sin x)^2

cos x * cos (4x) = sin x * sin (6x)

I fail when it comes to math XD

Oh, i know the process, but not the exact rules. There should be something in your text that (if memory serves cos(x)=1/(sin(x))) . . . or like that. Does the problem set have a goal (ie solve for X, or something like that)?

Memory does not serve. 1/sin(x) is cosec(x).

ruveyn

The first equation has mismatched parentheses, so there's no way we can guess what it is supposed to look like.

The second is pretty nasty. I might approach it from the angle that:
cos(A+B) = cos(A)*cos(B) - sin(A)*sin(B)

cos x * cos (4x) = sin x * sin (6x)
(cos (4x + x) + cos (4x - x)) / 2 = (cos (6x - x) - cos (6x + x)) / 2
cos 5x + cos 3x = cos 5x - cos 7x
cos 3x = -cos 7x
cos 3x + cos 7x = 0
2 cos ((7x + 3x)/2) cos ((7x - 3x)/2) = 0
cos 5x cos 2x = 0

cos 2x = 0 or cos 5x = 0
2x = 90 + 360n or 5x = 90 +360n
x = 45 + 180n or 18 + 72n

Nicely done, CloudWalker.

(I was far too out-of-practice to even start to solve it. )

I was aiming for the general idea, not the real thing . . . but, this stuff was a bit over 6 years ago for me and i haven't kept up with it since. ><

God I envy that.

Teach me sins and cosines that well.

I just discovered Euler's Identity recently, which is odd because I can deal with partial differential equations, bra-ket notation problems, diffeomorphic manifolds, group and set theory, etc.

Yet basic trig blows my mind right now, didn't pay enough attention to really learn it beyond a brute force level, the stuff is great.

Thanks and a late welcome too.

You must like Euler's Identity very much to use it as your avatar.

It is beautiful.

It shines when I consider it in my head, no stray edges, simple construction, obvious, yet still worth stating.