SOLUTION: Eliminate θ from these equation (i) x = sinθ + tanθ, y = sinθ - tanθ (ii) x = atanθ, y = bcosθ (iii) x = 1 + tanθ, y = cosθ

Question 1152029: Eliminate θ from these equation
(i) x = sinθ + tanθ, y = sinθ - tanθ
(ii) x = atanθ, y = bcosθ
(iii) x = 1 + tanθ, y = cosθ
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.

In my post, I will solve part (ii) only.

Start from the standard trigonometry identity

     = .            (1)



From the given part of  (ii),  

     =   and   = .     (2)



Now replace in (1)    by    and  replace    by  ,  based on (2).  You will get


     = .                 (3)


Thus we just eliminated    and obtained  the relationship  (the equation) for x and y.


The goal is reached:  the problem is just solved in this way.


You may simplify the equality  (4)  further as you want.

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