SOLUTION: If 8cosθ - 8sinθ = 3, find 55tanθ + 55/tanθ

Question 1209754: If 8cosθ - 8sinθ = 3,
find 55tanθ + 55/tanθ
Answer by ikleyn(52775) (Show Source): You can put this solution on YOUR website!
.
If 8cos(a) - 8sin(a) = 3, find 55tan(a) + 55/tan(a)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I will write letter 'a' everywhere instead of letter theta'.
It is because my text editor is not quite perfect.

We are given 

    8cos(a) - 8sin(a) = 3,

     cos(a) -   sin(a) = .


Square both sides

     cos^2(a) - 2cos(a)*sin(a) + cos^2(a) = .


Replace here  cos^2(a) + sin^2(a) by 1

     1 - 2cos(θ)*sin(a) = ,

     1 -  = 2cos(a)*sin(a),

      sin(2a) = .    (1)


From the other side hand,

    tan(a) +  =  =  = 

                            =  =  = .   (2)

           
Therefore, from (1) and (2) we have

    55tan(a) +  =  =  = 2*64 = 128.    ANSWER

Solved.

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