2 Trig Equations Answer one or the other is fine

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The discussion focuses on solving two trigonometric equations: Tan(x) = 3 tan(x/2) and sin(3x)cos(x) + cos(3x)sin(x) = 1, both within the interval 0 < x < 2π. Participants suggest using graphical methods to find intersections of the equations, which can provide insights into the solutions. Additionally, the use of trigonometric identities, such as the addition theorem, is recommended for simplifying the second equation. Reference to a 1954 CRC Mathematics Tables book is made for exact trig relationships that may assist in solving these equations. Overall, the conversation emphasizes the importance of graphical analysis and trigonometric identities in finding solutions.
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Tan(x)=3 tan(x/2) solve where 0<x<2pi?


sin3xcosx+cos3xsinx=1, where 0<x<2pi?



tried a long time...
 
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Hiya
what methods have you tried? A graphical method often leads to insights - plot the 2 graphs and see where they intersect. Then look for the reasons why and hey presto! the answer.
 
My old (1954) CRC Mathematics Tables book has exact trig relationships for tan x, tan 2x, and tan 3x. Also sin x, sin 2x, sin 3x, sin 4x and sin 5x. Also cosines. (page 344)
Bob S
 
BuffaloSoulja said:
Tan(x)=3 tan(x/2) solve where 0<x<2pi?


sin3xcosx+cos3xsinx=1, where 0<x<2pi?



tried a long time...
Hello BuffaloSoulja
The second looks very much like an addition theorem:
sin(alpha+beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta)
find alpha and beta and make the solution.
greetings Janm
 
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