CBSE Class 11-science Answered
given
m²+m' ²+2mm'cosø=1 ....................1
n² +n' ²+ +2nn'cosø=1 ..........................2
and mn + m'n'+(mn'+m'n)cosø=0...............3
tp....... m² +n² =cosec²ø.
from eq 1
(m' + mcosø)2 + m² -m²cos2ø = 1
(m' + mcosø)2 =1 - m² sin2ø.....................4
similarly
(n' + ncosø)2 = 1 - n² sin2ø......................5
now , (m' + mcosø)(n' + ncosø) = m' n' + (mn' + m' n )cosø + mncos2ø
= - mn + mncos2ø (from 3)
= -mn(1 - cos2ø ) = -mnsin2ø
squ both side
(m' + mcosø)2 (n' + ncosø)2 = m2 n2 sin4ø.............6
from eq4,5,&6
(1 - m² sin2ø)(1 - n² sin2ø ) = m2 n2 sin4ø
(m² + n2 )sin2ø = 1
or m² +n² =cosec²ø.