How to prove #sin(theta+phi)/cos(theta-phi)=(tantheta+tanphi)/(1+tanthetatanphi)#?
3 Answers
Please see the proof below
Explanation:
We need
Therefore,
Dividing by all the terms by
See Explanation
Explanation:
Let
Dividing by
Dividing by
hence proved.
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)sin(x+y)=sinxcosy+cosxsiny#
#•color(white)(x)cos(x-y)=cosxcosy+sinxsiny#
#"consider the left side"#
#=(sinthetacosphi+costhetasinphi)/(costhetacosphi+sinthetasinphi)#
#"divide terms on numerator/denominator by "costhetacosphi#
#"and cancel common factors"#
#=((sinthetacosphi)/(costhetacosphi)+(costhetasinphi)/(costhetacosphi))/((costhetacosphi)/(costhetacosphi)+(sinthetasinphi)/(costhetacosphi))=((sintheta)/costheta+sinphi/cosphi)/(1+sintheta/costhetaxxsinphi/cosphi#
#=(tantheta+tanphi)/(1+tanthetatanphi)#
#="right side "rArr"verified"#