Question

Let I (n)=2cos n x, $nϵN$, then I(1)I(n+1)-I(n)=___

• A. I(n+4)
• B. I(n+2)
• C. I(n+3)
• D. I(1)

Answer 1

The correct option is B

I(n+2)

I(n)=2 cos n x.
I(1)I(n+1)-I(n)=2 cosx. 2cos(n+1)x-2cos n x
=2[2 cos (n+1)x cos x-cosnx]
=2[cos (n+2)x+cos n x-cos nx]
=2 cos (n+2)x
=I(n+2)