# SOLUTION: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show s

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show s      Log On

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 Algebra: Linear Equations, Graphs, Slope Solvers Lessons Answers archive Quiz In Depth

 Question 30538: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work. Solve for t: 2t(sin(t2+1) + cos(t2+1))2 - 4tsin(t2+1)cos(t2+1) = 2. (Hint: remember that [sin(x)]2 is usually written sin2(x); now look for a trigonometric identity.)Answer by sdmmadam@yahoo.com(530)   (Show Source): You can put this solution on YOUR website!Solve for t: 2t(sin(t2+1) + cos(t2+1))2 - 4tsin(t2+1)cos(t2+1) = 2. 2t[sin(t^2+1) + cos(t^2+1)]^2 - 4tsin(t^2+1)cos(t^2+1) = 2. ----(1) Put (t^2+1) = y 2t(siny + cosy)^2 - 4tsinycosy = 2. t[(siny + cosy)^2 - 2sinycosy] = 2. t[(sin^2y+cos^2y +2sinycosy)- 2sinycosy] = 12 (using (a+b)^2 = a^2+b^2+2ab where here a =suny and b = cosy ) t[(sin^2y+cos^2y) +(2sinycosy- 2sinycosy)] = 2 ----(*) (by formula sin^2y+cos^2y = 1 ) t[(1)+0] = 2 tX(1) = 2 That is t = 2 Answer: t = 2 Remark: If you are wondering about the quantity y or for that matter (t^2+1), the terms in that quantity being of equal in magnitude and opposite in sign have got cancelled by the additive inverse law! as you can see in step (*)