Find P and `alpha` by converting equation `x+y =1` in ` xcos alpha + y sin alpha = P` form.

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of X -axis. Thinking Process : Equation of line which makes an angle alpha with positive side of X axis and whose length of perpendicular from origin p is given by x cos alpha+ y sin alpha = p .

Obtain equation of circle in Centre (sqrt(-4)cos alpha, 4 sin alpha) and radius 5.

Find the values of theta and p , if the equation x cos theta + y sin theta =p is the normal form of the line sqrt(3x) + y + 2=0 .

Transform the equation y = x tan alpha to polar form.

If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .

In R^(2) , find the unit vector orthogonal to unit vector bar(x) = ( cos alpha , sin alpha )

Find distance PQ between the points P ( a cos alpha, a sin alpha) and Q ( a cos beta, a sin beta) .

Q. Let p and q real number such that p!= 0 , p^2!=q and p^2!=-q . if alpha and beta are non-zero complex number satisfying alpha+beta=-p and alpha^3+beta^3=q , then a quadratic equation having alpha/beta and beta/alpha as its roots is

if [ ( cos alpha, - sin alpha),(sin alpha, cos alpha)] and A +A^1 =I then alpha =……