Question

If A = `[(tanx,cotx),(-cotx,tanx)]` and A + A' = 2I, then value of x ∈ `[0,pi/2]` is ______.

पर्याय

• 0

• `pi/3`

• `pi/4`

• `pi/2`

Answer 1

If A = `[(tanx,cotx),(-cotx,tanx)]` and A + A' = 2I, then value of x ∈ `[0,pi/2]` is `bbunderline(pi/4)`.

Explanation:

A + A' = 2I

⇒ `[(tanx,cotx),(-cotx,tanx)]+[(tanx,-cotx),(cotx,tanx)]=2[(1,0),(0,1)]`

⇒ `[(2tanx,0),(0,2tanx)]=[(2,0),(0,2)]`

⇒ 2tanx = 2

⇒ tanx = 1

⇒ x = `pi/4`