If `(cosx)/a=(cos(x+theta))/b=(cos(x+20))/c=(cos(x+3theta))/d` then `(a+c)/(b+d)` is equal to `a/d` (b) `c/b` (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)`