Find the area of the triangle whose vertices are : `(a cos alpha, b sin alpha), (a cos beta, b sin beta), (a cos gamma, b sin gamma)`

The orthocentre of triangle formed by (a cos alpha,a sin alpha),(a cos beta,a sin beta),(a cos gamma,a sin gamma) is

If origin is the orthocentre of the triangle with vertices A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then cos(2 alpha-beta-gamma)+cos(2 beta-gamma-alpha)+cos(2 gamma-alpha-beta)=

Delta ABC has vertices A(a cos alpha,a sin alpha),B(a cos beta,a sin beta) and C(a cos gamma,a sin gamma) then its orthocentre is

If (0,0) is orthocentre of triangle formed by A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then /_BAC=

If (0,0) is orthocentre of triangle formed by A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then /_BAC is

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)=

Without expanding evaluate the determinant |sin alpha cos alpha sin(alpha+delta)sin beta cos beta sin(beta+delta)sin gamma cos gamma sin(gamma+delta)|

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta) =

Without expanding evaluate the determinant det[[sin alpha,cos alpha sin(alpha+delta)sin beta,cos beta,sin(beta+delta)sin gamma,cos gamma,sin(gamma+delta)]]

Express the following in a + ib form: (a) ((cos alpha + i sin alpha)^(4))/((sin beta + i cos beta)^(5)) (b) ((1+ cos phi + i sin phi)/(1 + cos phi - isin phi))^(n) (c) ((cos alpha + i sin alpha)(cos beta + i sin beta))/((cos gamma + i sin gamma)(cos delta + i sin delta))