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"