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If 10cosA+5cosB+11cosC+14cosD=0 and 10sinA+5sinB-11sinC-14sinD=0 and cos(A+C) = m cos(B+D) n where m and n are co-prime,then the value of m+n = ? 2 Options: A)7 B)8 C)9 D)10 PLZ solve this Sir

If 
10cosA+5cosB+11cosC+14cosD=0
and
10sinA+5sinB-11sinC-14sinD=0
and
cos(A+C) =m
cos(B+D)   n
where m and n are co-prime,then the value of
m+n  = ?
  2
Options:
A)7   B)8  C)9  D)10
PLZ solve this Sir

Grade:11

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago

10cosA+11cosC=-5cosB-14cosD

10sinA-11sinC=5sinB+14sinD
Square both the equations and add them to get

221+ 220cos(A+C)= 221+140cos(B+D)
Find the value of cos(A+C)/COs(B+D) in the standard form such that the numnerator and the denominator shall not have any common facot.i.e. in the simplest form.
This will be equal to m/n and also, numerator=m and denominator=n

Find (m+n)/2 to get (C)


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