11. (i) Express sin4 A in the form p -\- q cos 2A + r cos 4A
(ii) Establish the identity
sinjij C) _ tan g __ tan q
cos B cos C
By applying this result successively to each term of the series
sin 9 sin 6 sin 9
cos 0 cos 20 cos 20 cos 30 cos 30 cos 40
or otherwise, show that the sum of n terms of this series is
sin n9
cos 0 cos (n + 1)0
12. (i) Find the equation of the tangent at the point where
x = —l on the curve y = x2 (x 1) (x — 3).
Show that this tangent touches the curve again and find the
coordinates of this second point of contact.
(ii) Find the area enclosed between the parabolas
y = x2 — 4x and y — 6x — x2.
(C41645)
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