If `1/(cosalpha cosbeta) +tanalpha tanbeta =tan gamma, ` show that `cos2gammale0`

If (1)/(cos alpha * cos beta )+ tan alpha * tan beta = tan gamma , where 0 lt gamma lt (pi)/2 and alpha , beta are positive acute angles , show that (pi)/4 lt gamma lt (pi)/2

(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=

(1+cosalphacosbeta)^2-(cosalpha+cosbeta)^2=

If cos(alpha + gamma)/cos(alpha - gamma) = cos 2beta then tan alpha, tan beta and tan gamma are

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is :

If cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0 , then the value of cos3alpha+cos3beta+cos3gamma is

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

If cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?