Prove that : cos3x +2 cos 5x + cos7x = cos5x
                      cosx + 2 cos3x + cos 5x      cos3x

Simplify and express the result in terms of a+ ib.
3(1-2i) -(-4-5i) + (-8+3i)

Find the equation of tangent and normal to the circle x2 + y2 = 25 at the point (-3,-4).

Find this equation of locus of points such that the sum of there distances from (0,2)&(0,-2) is 6.

If A+B+C = ?, prove that
cos2A+ cos2B - cos2C = 1 - 4 sinA sinB cosC.

          
Evaluate : i3 +1/i3

Find the equation of straight line passing through the orignal & parallel to the line 3x-2y + 1 = 0

Find the point of intersection of lines
x - 5y + 9 = 0 and 3x + 4y - 11 = 0;

                                                                                                                                          
Solve : sinx +Ö3 cosx = Ö2

Solve the inequations : x2 - 8x + 16 £0

Draw the graph of the solution set of the inequaions 2x + y ³ 2, x - y £ 1, x + y £ 8, x ³ 0 and y ³ 0.

In any DABC, prove that
a cos (B - C) = b + c sinA/2
                2

If 1, w, w2 be the cube root of unity, prove that
( 1 - w +w2 )5 + ( 1 - w +w2 )5 = 32

Sketch the graph of y = 3cos2x.

If the point (x,2) is equidistant from (8,-2) & (2,-2) find the value of x.

Evaluate :- cos [sin-1 3/5 + sin-1 5/13]

Find the value of K , so that the equation
x2 +kxy + y2 - 5x - 7y + 6 = 0 may represent a pair of straight lines.

Express in simplest form : tan-1     sinx
                                                            1 + cosx

Find the co-ordinance of a point which divides externally the joining (1,3) and (-3,9) in the ratio 1:3

                            
Find the angle between the straight lines whose joint equaion is x2 + 3xy + 2y2 = 0

                               
Show that the four points are concylic, pts are (1,0), (2,-7) , (8,1) (9,-6)

                                                
Find the equation of the circle through the intersection of circles x2 + y2 - 8x -2y + 7 = 0. And
x2 + y2 -4x + 10y +8 = 0 and that passes through the point (-1,-2)

If the angle of elevation of a cloud from a point h meter above a lake is b and the angle of
depression of its reflection in the lake is x. Prove that the height of the cloud is
h sin ( x+ b)
sin ( x- b)

Evaluate Ö 20 +Ö 20+ Ö 20+….¥

Solve x2 - 2x + 5    > 1
          3x2 - 2x - 5       2