" If "p=X cos0-Y sin0,q=X sin theta+Y cos

If quad X cos theta-Y sin theta,y=X sin theta+Y cos theta and x^(2)+4xy+y^(2)=AX^(2)+BY^(2)0<=theta<=(pi)/(2) then

Solve the following systems of homogenous equations: {:(x cos theta - y sin theta = 0),(x sin theta + y cos theta = 0):}

The equation of the locus of the point of intersection of the straight lines x sin theta + (1- cos theta) y = a sin theta and x sin theta -(1+ cos theta) y + a sin theta =0 is:

If x=a cos theta+b sin theta,y=a sin theta-b cos theta then show that y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0

If sin x sin h y = cos theta and cos x cos h y = sin theta then cos h^(2) y + cos^(2)x =

If x sin^(3) theta + y cos^(3) theta = sin theta cos theta ne 0 and x sin theta - y cos theta = 0 , then value of (x^(2) + y^(2)) is :

If x cos theta + y sin theta =2 and x cos theta - y sin theta =0 , then which one of the following is true ?

If f(x) = [(cos theta, - sin theta, 0),(sin x, cos x , 0),(0,0,1)] , show that F(x) F(y) = F(x + y) .

If x=r cos0 and y=r sin0 , then show that (d y)/(dx)+(x)/(y)=0 .