prove that `(cos3theta+cos3phi)/(2cos(theta+phi)-1)`=`(costheta +cosphi)cos(theta+phi)-(sintheta+sinphi)sin(theta+phi)`

Prove that: cos2 theta*cos2 phi+cos^(2)(theta+phi)-cos^(2)(theta-phi)=cos(2 theta+2 phi)

cos2 theta cos2 phi+sin^(2)(theta-phi)-sin^(2)(theta+phi)=cos(2 theta+2 phi)

cos 2 (theta+ phi) +4 cos (theta + phi ) sin theta sin phi + 2 sin ^(2) phi=

cos 2 (theta+ phi) +4 cos (theta + phi ) sin theta sin phi + 2 sin ^(2) phi=

Compute the following: {:[(sin(theta+phi), cos(theta+phi)),(sin(theta - phi),cos(theta-phi))] +[(sin(theta-phi), cos(theta-phi)),(sin(theta+phi), cos(theta+phi))]

" If "|{:(sin theta cos phi,,sin theta sin phi,,cos theta),(cos theta cos phi,, cos theta sin phi,,-sin theta),(-sin theta sin phi,,sin theta cos phi,,theta):}| then

" If "|{:(sin theta cos phi,,sin theta sin phi,,cos theta),(cos theta cos phi,, cos theta sin phi,,-sin theta),(-sin theta sin phi,,sin theta cos phi,,theta):}| then

" If "|{:(sin theta cos phi,,sin theta sin phi,,cos theta),(cos theta cos phi,, cos theta sin phi,,-sin theta),(-sin theta sin phi,,sin theta cos phi,,theta):}| then

Prove that (sin(theta+phi)-2sintheta+sin(theta-phi))/(cos(theta+phi)-2costheta+cos(theta-phi))=tantheta

Prove that, cos^(2) (theta + phi) - sin^(2) (theta - phi) = cos 2 theta cos 2 phi