" If "3tan theta tan varphi=1." Prove that "2cos(theta+varphi)=cos(theta-varphi)

If 3tanthetatanvarphi=1 , then prove that 2cos(theta+varphi)=cos(theta-varphi) .

If 3tan theta tan phi=1. Prove that 2cos(theta+phi)=cos(theta-phi)

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+varphi)=cos (theta-varphi) .

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+varphi)=cos (theta-varphi) .

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+phi)=cos (theta-phi) .

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+phi)=cos (theta-phi) .

If 3tan theta tan phi=1, then prove that 2cos(theta+phi)+cos(theta-phi)=0

If t a n^2theta=2t a n^2varphi+1 , prove that cos2theta+ sin^2varphi=0.

If sin theta+sin varphi=a and cos theta varphi+cos varphi=b then cos((theta-varphi)/(2))=+-(1)/(2)sqrt(a^(2)+b^(2))cos((theta-varphi)/(2))=+-sqrt(a^(2)-b^(2))tan((theta-varphi)/(2))=+-sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))cos(theta-varphi)=(a^(2)+b^(2)-2)/(2)

If t a n^2theta=2t a n^2varphi+1 , prove that cos2theta+sin^2phi =0.