If `P(x)=[cosxsinx-sinxcosx]` , then show that `P(x)\ P(y)=P(x+y)=P(y)\ P(x)` .

If P(x)=[cos x sin x-sin x cos x], then show that P(x)P(y)=P(x+y)=P(y)P(x)

If P(x)=[[cos x,sin x-sin x,cos x]] then show that P(x)P(y)=P(x+y)=P(y)P(x)

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

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

If p(x)=[{:(cosx,sinx),(-sinx,cosx):}] then show that p(x)*p(y)=p(x+y) .

If x^(p)y^(q)=(x+y)^(p+q) , then prove that (dy)/(dx)=(y)/(x) .

If the origin is shifted to (h,k) by translation of axes . then the Co-ordinates of a point P(x,y) are transformed as P(x', y') = O P(x+h, y+k) O P(x-h, y-k) O P(x'– h, y' - k) O P(x' – h, y' +k)

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.

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