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If A = [cos⁡𝑥−sin⁡𝑥sin⁡𝑥cos⁡𝑥] and A + A' = I, then the value of x ∈ [0,π2] is ______.

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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
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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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2025-2026 (March) 65/2/1
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