If P(x)=[(cosx, sinx),(-sinx, cosx)] , then show that P(x).P(y)=P(x+y)=P(y).P(x) .

If x ,y,z are in A.P. show that (xy)^(-1) , (zx)^(-1) , (yz)^(-1) are also in A.P.

If x, y, z are in A.P. and tan^(-1) x, tan^(-1) y and tan^(-1)z are also in A.P. then show that x=y=z and y≠0

If a ,b ,c ,d are in A.P. and x , y , z are in G.P., then show that x^(b-c)doty^(c-a)dotz^(a-b)=1.

If a ,b ,c ,d are in A.P. and x , y , z are in G.P., then show that x^(b-c)doty^(c-a)dotz^(a-b)=1.

For any sets X and Y prove that P(X) cup P(Y) sub P(X cup Y)

If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that (y+z)/(x) , (z+x)/(y) , (x+y)/(z) are in A.P.

Let f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h e r ep is a constant. Then (d^3)/(dx^3)(f(x)) at x=0 is p (b) p-p^3 p+p^3 (d) independent of p

If P is a point (x ,y) on the line y=-3x such that P and the point (3, 4) are on the opposite sides of the line 3x-4y=8, then

If the straight line represented by x cos alpha + y sin alpha = p intersect the circle x^2+y^2=a^2 at the points A and B , then show that the equation of the circle with AB as diameter is (x^2+y^2-a^2)-2p(xcos alpha+y sin alpha-p)=0