March 16th, 2017, 08:57 AM  #1 
Senior Member Joined: Jul 2016 From: USA Posts: 108 Thanks: 13  Simplify: sin(x)+tan(x)
Pretty simple simplification problem here. Can sin(x)+tan(x) be simplified to where there is only one "x" appearing in the expression rather than two "x"s? For example sin(x)/cos(x) can be reduced to tan(x) where there is only one "x" appearing in the expression. Also, I wanted to bring up another question for those who are still with me. Is there a specific field of math that deals with manipulating expressions such that there is only 1 of a certain variable appearing. For instance: x^2 + x =x^2 + x/2 + x/2 =x(x+1/2) + x/2 =x(x+1/2) +1/2(x+1/2)  1/4 =(x + 1/2)(x + 1/2)  1/4 =(x + 1/2)^2  1/4 Here, I manipulated the expression such that x only appears once. Is there a specific field of math that deals with challenges like these? It would be in the category of algebra, I suppose, but a more specific form of algebra. Hope that makes sense. Thanks! 
March 16th, 2017, 10:28 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,656 Thanks: 1327 
I don't believe one can state the expression $sin{x}+\tan{x}$ in terms of a single trig function ... if possible, it would already exist on a list of identities.


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simplify, sinx, tanx 
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