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

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)