The distance between the points `(a cosalpha, a sinalpha)` and `(a cosbeta, a sinbeta)` where a> 0

Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a\ cosalpha,\ a\ sinalpha)a n d\ (a\ cosbeta,\ asinbeta)dot

If the points A(0,0),B(cosalpha,sinalpha) , and C(cosbeta,sinbeta) are the vertices of a right- angled triangle, then

The points A(0,0),B(cosalpha,sinalpha) and C(cosbeta,sinbeta) are the vertices of a right-angled triangle then

If xcosalpha+ysinalpha=xcosbeta+ysinbeta=2a then cosalpha cosbeta=

Evaluate the following: |[cosalpha, sinalpha],[sinalpha, cosalpha]|

Find the amplitude of sinalpha+i(1-cosalpha)

sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

Show without expanding at any stage that: | (1,cosalpha-sinalpha, cosalpha+sinalpha),(1,cosbeta-sinbeta,cosbeta+sinbeta),(1, cosgamma-singamma,cosgamma+singamma)| =2 |(1,cosalpha, sinalpha),(1,cosbeta, sinbeta),(1,cosgamma,singamma)|