(i) show that tan 15° = 2 – √3,
(ii) solve, for 0 < x < 360°,
cosec 4x - cot 4x = 1
(a) Show that
f(x) = 5/[2x + 1)(x - 3)]
The curve C has equation y= f (x). The point P(-1, 5/2) lies on C.
(b) Find an equation of the normal to C at P.
8. (a) Express 2cos 3x – 3sin 3x in the form R cos (3x + α), where R and α are constants, R > 0, 0 <& alpha; < π/2. Give your answers to 3 significant figures.
f(x) = e2x cos3x
(b) Show that f ′(x) can be written in the form
f'(x) = Re2x cos(3x + α)
where R and α are the constants found in part (a).
(c) Hence, or otherwise, find the smallest positive value of x for which the curve with equation y = f (x) has a turning point.
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