Question

If A = `[(cos x, -sinx),(sinx, cos x)]` and A + A' = I, then the value of x ∈ `[0, π/2]` is ______. 

विकल्प

• 0

• `π/4`

• `π/3`

• `π/2`

Answer 1

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`