2.69: Tangent to 7+tanx7 + \tan x and a derivative equation

0606/23/O/N/16 — Question 6 · 8 marks

A curve has equation y=7+tanxy = 7 + \tan x. Find
(i)
the equation of the tangent to the curve at the point where x=π4x = \dfrac{\pi}{4},
[4]
(ii)
the values of xx between 00 and π\pi radians for which dydx=y\dfrac{\mathrm{d}y}{\mathrm{d}x} = y.
[4]