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Question
If A= `[(cos alpha, -sin alpha), (sin alpha, cos alpha)]` then A + A' = I then the value of α is ______.
Options
`pi/6`
`pi/3`
`pi`
`(3pi)/2`
Solution
If A= `[(cos alpha, -sin alpha), (sin alpha, cos alpha)]` then A + A' = I then the value of α is `underline(pi/3)`.
Explanation:
`A = [(cos alpha , -sin alpha),(sin alpha , cos alpha)], A' = [(cos alpha , sin alpha),(-sin alpha, cos alpha)]`
`therefore A + A' = I`
`[(cos alpha, - sin alpha),(sin alpha, cos alpha)] + [(cos alpha , sin alpha), (- sin alpha, cos alpha)] = [(1,0), (0,1)]`
`=> [(cos alpha + cos alpha, -sin alpha + sin alpha), (sin alpha - sin alpha, cos alpha + cos alpha)] = [(1,0),(0,1)]`
`=> [(2 cos alpha, 0), (0, 2 cos alpha)] =[(1,0), (0,1)]`
`=> 2 cos alpha = 1/2`
`=> cos alpha = cos pi/3`
`therefore alpha = pi/3`
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