If `lambda and alpha` are real numbers and lines `lambda x + sin (alpha)y + cos alpha = 0, x + cos (alpha)y + sin alpha=0, and -x+ sin (alpha) y-cos alpha = 0` are concurrent. Find range of `alpha`, if `lambda=1?`

If x sin ^3 alpha + y cos^3 alpha = sin alpha cos alpha and x sin alpha - y cos alpha =0 , then x^2 +y^2 is

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

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

If the lines lambda x+(sin alpha)y+cos alpha=0,x+cos alpha y+sin alpha=0,x-sin alpha y+cos alpha= pass through the point where alpha in R the lambda lies in the interval

If the lines lambda x+(sin alpha)y+cos alpha=0,x+(cos alpha)y+sin alpha=0,x-(sin alpha)y+cos alpha=0 pass through the same point where alpha in R then lambda lies in the interval

Let lambda and alpha be real. Find the set of all values of lambda for which the system of linear equations lambdax + ("sin"alpha)y + ("cos" alpha)z =0 , x + ("cos"alpha)y + ("sin" alpha) z =0 and -x + ("sin" alpha)y -("cos" alpha)z =0 has a non-trivial solution. For lambda =1 , find all values of alpha .

If x sin ^ (3) alpha + y cos ^ (3) alpha = sin alpha cos alpha and x sin alpha-y cos alpha = 0 then x ^ (2) + y ^ (2) =

The locus of the intersection point of x cos alpha+y sin alpha=a and x sin alpha-y cos alpha=b is