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

If x=(sin p)/(cos^(2)p),y=(cos p)/(sin^(2)p) and sin p+cos p=(1)/(2) ,then find the value of (44)/((x+y))

If cos(x-y),cos x and cos(x+y) are in H.P.are in H.P.then cos x*sec((y)/(2))=

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

If y^(2)=P(x) is a polynomial of degree 3, then 2((d)/(dx))(y^(3)(d^(2)y)/(dx^(2))) is equal to P^(x)+P'(x) (b) P^(x)P^(x)P(x)P^(x)(d) a constant