If `|(cos(A+B),-sin(A+B),cos2B),(sinA,cosA,sinB),(-cosA,sinA,cosB)|=0` then B =

Options

A. `(2n + 1)pi//2, n in Z`
B. `npi, n in Z`
C. `(2n + 1) pi, n in Z`
D. `2n pi, n inZ`

Answer

A

Explanation

We have,
`|{:("cos" (A+B), -"sin"(A+B), "cos" 2B),("sin"A, "cos"A, "sin"B), (-"cos"A, "sin"A, "cos"B):}|=0`
`rArr "cos"^(2) (A+B) + "sin" (A+B) + "cos" 2B xx ("sin"^(2)A + "cos"^(2)A) = 0`
`rArr "cos"2B + 1 =0`
`rArr "cos" 2B = -1 ="cos" pi`
`rArr 2B = 2n pi +- pi, n inZ`
`rArr B = (2n +-1) pi//2, n in Z`
Hence, option (a) is correct