1. If ^n = a_n - b_n \sqrt{3})
for all positive integers n, where 
and integers, show that
(i)
(ii) Calculate
for n=1, 2 and 3.
(iii) Guess a formula for
and prove your guess is true for all positive integers n.
2. Show that^5 = \sum_{r=0}^5 \ ^5C_rcos^{5-r}\theta \ sin^r \theta)
3. The angles of elevation of the top of a tower P measured from three points A, B, and C are
respecitvely.
A, B and C are in a straight line such that AB = BC = a, but the line AC does not pass through S, the base of the tower.
(i) If
show that:
(ii) prove that the height of the tower is:
^{1/2}})
4. If a>0, b>0 and c>0 show that:
^{1/3})
(i)
(ii) Calculate
(iii) Guess a formula for
2. Show that
3. The angles of elevation of the top of a tower P measured from three points A, B, and C are
A, B and C are in a straight line such that AB = BC = a, but the line AC does not pass through S, the base of the tower.
(i) If
(ii) prove that the height of the tower is:
4. If a>0, b>0 and c>0 show that:
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