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If cosx/a=cos(x+theta)/b=cos(x+2theta)/c...

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`

A

`(a)/(d)`

B

`(C)/(b)`

C

`(b)/(c)`

D

`(d)/(a)`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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