Trignometry question involving Tan

[babak13]

I have tried so much to solve this but i can do only until r sin θ but i can not do the rest, i will appreciate if anyone can help. i have attached the image of the question.
thanks

 

[DrPhil]

I have tried so much to solve this but i can do only until r sin θ but i can not do the rest, i will appreciate if anyone can help. i have attached the image of the question.
thanks

Point A travels around a circle. In (x,y) coordinates measured from O,
x = r cosθ,......y = r sinθ

Let point D be where a perpendicular from A hits the x-axis.
What is the distance DB ?

EDIT: OOPS - after reading Subhotosh Kahn's reply, I see that I did what he warned against - used "x" to mean something different than the problem drawing.

 

[Deleted member 4993]

I have tried so much to solve this but i can do only until r sin θ but i can not do the rest, i will appreciate if anyone can help. i have attached the image of the question.
thanks

Be careful here about using x as distance along axis OB - because in your problem AB is defined as x.

do you see that

r*cos(Θ)+x*cos(α) = a.................... and

x*sin(α) = r*sin(Θ)