2 Trig Equations Answer one or the other is fine

[BuffaloSoulja]

Tan(x)=3 tan(x/2) solve where 0<x<2pi?


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



tried a long time...

 

[arithmetix]

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.

 

[Bob S]

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

 

[JANm]

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