If ( 1 + x ) ^(n) = a(0) + a (1) x + ...

If ` ( 1 + x ) ^(n) = a_(0) + a _(1) x + a_(2) x^(2) + ………. + a_(n)x^(n) ` , then show that
(i) ` a_(0) - a_(2) + a_(4) - a_(6) + ……… = 2^(n//2) cos . (npi)/4 `
(ii) ` a _(1) a_(3) + a_(5) - a_(7) + …….. = 2^(n//2) sin . (npi)/4 `

A

`2^(n)`

B

`2^(2n)`

C

`(2^(n))/(2)`

D

`2^((n)/(2))`

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The correct Answer is:

D

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