Sir/Mam plz help in Trigonomatric functions

Asked by  | 10th Jun, 2008, 05:37: AM

Expert Answer:

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)=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.

Answered by  | 17th Jun, 2009, 07:07: PM

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