Coordinates of the foot of the perpendicular drawn from 0,0 to he line jolning `(a cos alpha, a sin alpha) and (a cos beta, a sin beta)` are

Perpendicular from the origin to the line joining the points (c cos alpha,c sin alpha) and (c cos beta,c sin beta) divides it in the ratio

Perpendicular from the origin to the line joining the points (c cos alpha,c sin alpha) and (c cos beta,c sin beta) divides it in the ratio

The perpendicular from the origin to the line joining the points A(a cos alpha, a sin alpha) and B(a sin beta, a cos beta) divides AB in the ratio

Evaluate: quad =|0sin alpha-cos alpha-sin alpha0sin beta cos alpha-sin beta0

Evaluate Delta=|[0, sin alpha, -cos alpha],[ -sin alpha, 0 , sin beta],[ cos alpha, -sin beta, 0]|

Find |A| , if A =[{:( 0 , sin alpha , cos alpha),(sin alpha , 0 , sin beta),(cos alpha , -sin beta , 0):}]

If origin is the orthocenter of a triangle formed by the points (cos alpha*sin alpha,0)*(cos beta,sin beta.0),(cos gamma,sin gamma,0) then sum cos(2 alpha-beta-gamma)=

Evaluate : |{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 , sin beta) , (cos alpha , -sin beta , 0):}|

If cos alpha+cos beta=0=sin alpha+sin beta then cos2 alpha+cos2 beta=