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Question
If A = `[(cos x, -sinx),(sinx, cos x)]` and A + A' = I, then the value of x ∈ `[0, π/2]` is ______.
Options
0
`π/4`
`π/3`
`π/2`
MCQ
Fill in the Blanks
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Solution
If A = `[(cos x, -sinx),(sinx, cos x)]` and A + A' = I, then the value of x ∈ `[0, π/2]` is `bbunderline(π/3)`.
Explanation:
A = `[(cos x, -sinx),(sinx, cos x)]`
A + A' = I
`[(cos x, -sinx),(sinx, cos x)]+[(cosx, sinx),(-sinx, cosx)]`
= `[(1,0),(0,1)]`
= `[(2cosx, 0),(0, 2cosx)]`
= `[(1,0),(0,1)]`
2 cos x = 1
cos x = `1/2`
cosx = cos `π/3`
x = `π/3`
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