If `cosx/a=cos(x+theta)/b=cos(x+2theta)/c=cos(x+3theta)/d` then `(a+c)/(b+d)` is equal to `(A)a/d (B)c/d (C)b/c (D)d/a`

Options

A. `(a)/(d)`
B. `(C)/(b)`
C. `(b)/(c)`
D. `(d)/(a)`

Answer

C

Explanation

For each of the ratios be 1/k.
`(a+c)/(b+d)=(k cos x+k cos(x+2B))/(k cos(x+theta)+k cos(x+3theta))`
`=(2cos(x+theta)cos theta)/(2cos(x+2theta)cos theta)`
`=(cos(x+theta))/(cos(x+2theta))=(b)/(c)`