The triangle `ABC` has a right angle at `B, \ ∠BAC = theta` and `AB = 6`. The line `BD` is drawn perpendicular to `AC`. The line `DE` is then drawn perpendicular to `BC`. This process continues indefinitely as shown in the diagram.
- Find the length of the interval `BD`, and hence show that the length of the interval `EF` is `6 sin^3\ theta`. (2 marks)
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- Show that the limiting sum
`qquad BD + EF + GH + ···`
is given by `6 sec\ theta tan\ theta`. (3 marks)
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