Solving Trigonometric Equations: What is the Best Way?

[phymatter]

while solving trigonometric equations many times we get answer in different forms depending on the way in which we solve the problem , so what is the best way to ascertain that all the answers are the same ??
pl. help!

 

[CompuChip]

Do you mean, that you might get the answer as 2 cos(x) sin(x), or as sin(2x) ?

One thing you could do, besides trying to use algebraic identities to transform one into the other, is plug in some values (for example $0, \pi/12, 2\pi/12, 3\pi/12, \ldots, \pi$) or draw the graphs of the two expressions (for example, http://www.wolframalpha.com/input/?i=plot+2+cos(x)+sin(x)+and+sin(2x)).

 

[raam86]

Hi, I hope I got your question right. Due to the nature of trig' functions as seen in the Unit Circle (wiki for more info). so sin30=1/2 but sin150=1/2 as well. The simple identity for this is sinx=a+180k,a