SECTION A

Question 1

Show that cos 5x = 16 cos⁵x - 20 cos³x + 5 cosx

Express in ( x+iy) and find the conjugate & Modulus of

   Ö3 - i Ö2
2Ö3 - iÖ2

Find the point equidistant from the points (6,2), (-1,3) & (-3,-1)

If x = (a+b), y = (aw +bw²) and 3=(aw² + bw) where w is a cube root of unity, prove that: x³ + y³ + z³ = 3( a³ + b³).

Reduce the equation Ö3x + y + 2 = 0 to :
1) Slope intercepts forms & find the slope & y intercept;
2)Normal form and find p and x.

Find the coordinates of foot of perpendicular draw from the pts (2,3) on the line y = 3x +4

Show that x² + 6xy + 9y² + 4x +12y - 5 = 0 represents two parallel straight lines and also find the distance between these lines.

Find the square root of : 3-4i

If A + B + C =prove that
cos A/2 + cos B/2 + cos C/2 = 4 cos (- A/4) cos ( - B/4 ) cos ( - C/4 )
                                                                                                                

Show that the locus of complex variable z, satisfying

Solve : tanx + tan2x + tan3x = tanx tan2x tan3x.

Find the equation of tangent and normal to the circle x² +y² - 2ax = 0 at the point ( a(1+cosa), a sina).

In any D ABC, prove that;

a³ cos(B-C) + b³ cos(C-A) +c³ cos(A-B) = 3abc

Find the area of a D, the coordinates of the mid points of whose sides are (-1,-2), (6,1) & (3,5) restyle.

Determine the ratio in which y - x+2 = 0 divides the line joining (3-1) and (8,9)

Find the equation of right bisector of the segment joining A(1,1) and B92,3).

Draw the graph of the solution set of the inequations 2x+y³2, x-y£1, x +2y £ 8, x ³0 and y ³0.

Find all real values of x for which x-2         x-3
                                                            ----   <   ----
                                                           3x+1     3x-2

Find the equation of the circle whose center lies on the line x-4y = 1 and which passes through the point (3,7) and (5,5).

Show that the straight lines
x²(tan²Q + cos²Q) - 2xy tanQ + y² sin²Q = 0 makes angles with x-axis such that the difference of their tangents is 2.

A spherical balloon whose radius is 4cm, subtends at an observer's eye an angle a, when an angular elevation of the center is b. Determine the height of the center of the balloon.

Sketch the graph of y = cos²x.

Simplify :

tan-1		Ö1+x2 + Ö1-x2    Ö1+x2 - Ö1-x2

slovle : 2tan^-1 (cosX) = tan^-1 (2cosecx)

Find the equation of the circle cutting orthogonal the three circles x² + y² - 2x +3y - 7 = 0,
x² + y² + 5x-5y + 9 = 0, and x² + y² + 7x - 9y + 29 = 0,