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

if xcosalpha+ysinalpha=k=xcosbeta+ysinbeta ,show that x/(cos((alpha+beta)/2))=y/(sin((alpha+beta)/2))=k/(cos((alpha-beta)/2))

Prove that the area of the parallelogram formed by the lines xcosalpha+ysinalpha=p ,xcosalpha+ys inalpha=q ,xcosbeta+ysinbeta=ra n dx cosbeta+ysinbeta=si s+-(p-q)(r-s)cos e c(alpha-beta)dot

Find the condition so that the lines xcosalpha+ysinalpha=p,xcosbeta+ysinbeta=qandy=xtantheta be concurrent.

If sinalpha + sinbeta + singamma = 3 , then cosalpha + cosbeta + cosgamma equals :

If cosalpha=cosbeta , then alpha+beta= ____

Evaluate |[cosalpha cosbeta,cosalpha sinbeta,-sinalpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta,sinalpha sinbeta,cosalpha]|

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)|

(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2 =