if `A=|(1+cosalpha,1+sinalpha,1),(1+cosbeta,1+sinbeta,1),(1,1,1)|!=0` then

If A=|(1+cosalpha,1+sinalpha,1),(1+cosbeta,1+sinbeta,1),(1,1,1)|ne0 , then :

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)|

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)|

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

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

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

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

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

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :

If A=[{:(sinalpha,-cosalpha,0),(cosalpha,sinalpha,0),(0,0,1):}] then A^(-1) is equal to