Prove that the area of triangle whose vertices are (acosp, bsinp) , (acosq,bcosq),(acosr,bsinr) is 2absin(p - q / 2)sin(q - - Maths - Introduction to Three Dimensional Geometry

Question

Prove that the area of triangle whose vertices are (acosp, bsinp) ,
(acosq,bcosq),(acosr,bsinr) is 2absin(p - q / 2)sin(q - c / 2)sin(r
- p / 2)

Brijendra Pal · Accepted Answer

Hi, area of triangle =12 acospbsinp1acosqbsinq1acosrbsinr1=12×abcospsinp1cosqsinq1cosrsinr1=12×abcospsinq-sinr-sinpcosq-cosr+sinrcosq-cosrsinq=ab2cospsinq-sinpcosq+sinpcosr-cospsinr+sinr-q=ab2sinp-q+sinp-r+sinr-qRegards

Prove that the area of triangle whose vertices are (acosp, bsinp) , (acosq,bcosq),(acosr,bsinr) is 2absin(p - q / 2)sin(q - c / 2)sin(r - p / 2)