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If A(x)={:[(e^(x),e^(x)),(e^(-x),e^(-x))...

If `A(x)={:[(e^(x),e^(x)),(e^(-x),e^(-x))]:}` then A(x) A(y)=

A

A(x+y)A(x-y)

B

A(x+y)+A(x-y)

C

A(x+y)-A(x-y)

D

A(x+y)

Text Solution

Verified by Experts

The correct Answer is:
B
`A(x)={:[(e^(x),e^(x)),(e^(-x),e^(-x))]:}`
`A(y)={:[(e^(y),e^(y)),(e^-y,e^(-y))]:}`
`A(x)A(y)={:[(e^(x+y)+e^(x-y),e^(-x)e^(y)+e^(x)e^(-y)),(e^(-x)e^(y)+e^(-x)e^(-y),e^(-x)e^(y)+e^(-x)e^(-y))]:}`
`{:[(e^(x+y)+e^(x-y),e^(x+y)+e^(x-y)),(e^(-x+y)+e^(-x-y),e^(-x+y)+e^(-x-y))]:}`
`{:[(e^(x+y)+e^(x-y),e^(x+y)+e^(x-y)),(e^(-(x-y))+e^(-(x+y)),e^(-(x-y))+e^(-(x+y)))]:}`
=A(x+y)+A(x-y).
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