Question 1 Show that (frac{1}{tan theta+cot theta}=sin theta cos theta). [3] Question 2 Find the coordinates of the points where the line (2 y=x-1) meets the curve (x^{2}+y^{2}=29). [5] Question 3 (i) Express (log _{x} 2) in terms of a logarithm to base 2. [1] (ii) Using the result of part (i), and the substitution … Read more
Question 1 Solve the inequality (x(2 x-1)>15) [3] Question 2 (i) Given that (y=(12-4 x)^{5},) find (frac{ d y}{ d x}). (ii) Hence find the approximate change in (y) as (x) increases from 0.5 to (0.5+p,) where (p) is small. [2] Question 4 Without using a calculator, find the positive root of the equation[(5-2 sqrt{2}) … Read more
1. Show that (frac{1}{1-cos theta}+frac{1}{1+cos theta}=2 operatorname{cosec}^{2} theta). [3] Answer 2. Express (lg a+3 lg b-3) as a single logarithm. [3] Answer 3. (a) Shade the region corresponding to the set given below each Venn diagram. (b) Given that (P=left{p: tan p=1right.) for (left.0^{circ} leqslant p leqslant 540^{circ}right}), find (n (P)). Answer 4. (a) Solve … Read more
Show that \(\frac{1}{1-\cos \theta}+\frac{1}{1+\cos \theta}=2 \operatorname{cosec}^{2} \theta\).