How solve this trigo system ?

01312020, 10:48 PM
Post: #12




RE: How solve this trigo system ?
(09182017 08:56 AM)ggauny@live.fr Wrote: cos x  cos y = 1/2 Nice problem ! Square both side, both equations: \( \cos^2 x  2 \cos x \cos y + \cos^2 y = 1/4 \) \((1\cos^2 x)(1\cos^2 y) = 1  (\cos^2 x + \cos^2 y) + (\cos^2 x \cos^2 y) = 9/64 \) Add both equations, and simplify: \((\cos x \cos y)^2  2( \cos x \cos y) + 39/64 = 0 \quad\; → \cos x \cos y = 3/8\) Using angle sum formula, we have: \(\cos(x + y) = \cos x \cos y  \sin x \sin y = 0 \quad\quad → x + y = ±\,90° \) This meant we can replace sin(y) as ±cos(x) 2 sin(x) cos(x) = sin(2x) = ±3/4 The process of squaring may introduce some bad solutions. With those eliminated, we have x ≈ ±24.295°, ±114.295° These solutions corresponded to y ≈ ±65.705°, ±155.705° 

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Messages In This Thread 
How solve this trigo system ?  ggauny@live.fr  09182017, 08:56 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09182017, 10:12 AM
RE: How solve this trigo system ?  ggauny@live.fr  09182017, 10:45 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09182017, 10:55 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09182017, 11:28 AM
RE: How solve this trigo system ?  Dieter  09182017, 12:46 PM
RE: How solve this trigo system ?  Dieter  09182017, 05:48 PM
RE: How solve this trigo system ?  AlexFekken  09192017, 06:36 AM
RE: How solve this trigo system ?  Albert Chan  01312020 10:48 PM
RE: How solve this trigo system ?  Dieter  09192017, 06:30 PM
RE: How solve this trigo system ?  ggauny@live.fr  09222017, 07:27 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09222017, 05:05 PM

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