The discussion revolves around solving a trigonometric equation involving the tangent function, specifically in the context of finding the value of x in the equation tan(x) = ((1 + tan(1))(1 + tan(2)) - 2) / ((1 - tan(1))(1 - tan(2)) - 2). Participants explore various algebraic manipulations and trigonometric identities to simplify the expression.
Several participants have provided guidance on how to manipulate the equation further, with some suggesting specific forms to aim for. There is an ongoing exploration of potential simplifications and substitutions related to trigonometric identities, but no consensus has been reached on a final method or solution.
Participants note the ambiguity regarding whether the angles are in radians or degrees, which may affect the interpretation of the problem. Additionally, there are indications of imposed homework constraints that guide the discussion towards algebraic manipulation rather than direct solutions.
Is that really tan(1) and tan(2), as in 1 and 2 radians?diredragon said:Homework Statement
##tanx=\frac{(1+tan1)(1+tan2)-2}{(1-tan1)(1-tan2)-2}## find x
Homework Equations
3. The Attempt at a Solution [/B]
I tried multiplying through the parentheses and arrived at ##tanx=\frac{(tan1tan2-1)+(tan2+tan1)}{(tan1tan2-1)-(tan2+tan1)}## and i don't know if this is any simpler than what was originally set. Is there a trigonometric identity at play here?
It's in degrees. So i divided both num and den by ##tan1tan2 - 1## and i getSammyS said:Whatever it is, divide the numerator & denominator by ##\ tan1\,tan2 -1 \ ##.
##tanx=\frac{1-tan3}{1+tan3}## but that's as far as the simolification goes right? Now the use of calculator is required. It says that the answer is ##x=42## in degrees.NascentOxygen said:Ask google to search on tan(a+b) (or some trig expression like that) and see whether you can substitute something for that expression you have for the term I designated by A.