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Let f(n)=2cosn xAAn in N , then f(1)f(n...

Let `f(n)=2cosn xAAn in N ,` then `f(1)f(n+1)-f(n)` is equal to `f(n+3)` (b) `f(n+2)` `f(n+1)f(2)` (d) `f(n+2)f(2)`

A

`f(n+3)`

B

`f(n+2)`

C

`f(n+1)f(2)`

D

`f(n+2)f(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(n)=2cos nx`
`rArr f(1)f(n+1)-f(n)`
`=4cos x cos(n+1)x-2cos nx`
`=2[2cos (n+1)x cos x-cos nx]`
`=2[cos(n+2)x+cos nx-cosnx]`
`=2cos(n+2)x=f(n+2)`.
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