Eliminate `theta` from the following equations: `x sin alpha + ycosalpha = p and x cos alpha-y sin alpha = q`

If x=a sin alpha+b cos alpha and y=a cos alpha-b sin alpha then remove alpha

If p & q are lengths of perpendicular from the origin x sin alpha + y cos alpha = a sin alphacos alpha and x cos alpha-y sin alpha = acos 2alpha, then 4p^2 + q^2

Eliminate alpha between the equations: (sin^2 alpha)/(cos alpha)=a^3 and (cos^2 alpha)/(sin alpha)= b^3 .

If p&q are lengths of perpendicular from the origin x sin alpha+y cos alpha=a sin alpha cos alpha and x cos alpha-y sin alpha=a cos2 alpha, then 4p^(2)+q^(2)

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

Eliminate alpha , if x = r cos alpha , y = r sin alpha .

Eliminate alpha , if x = r cos alpha , y = r sin alpha .