Question

The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.

Options

• `[(1,cos alpha),(- cos alpha, -1)]`

• `- sec^2 alpha [(1, - cos alpha),(- cos alpha, 1)]`

• `cosec^2 alpha [(1,cos alpha),(- cos alpha, -1)]`

• `cosec^2 [(1,- cos alpha),(- cos alpha, 1)]`

Answer 1

The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is `underline(cosec^2 alpha [(1,cos alpha),(- cos alpha, -1)])`.

Explanation:

`"A"^-1 = 1/|"A"| ("adj" "A")`

`= 1/(- 1 + cos^2alpha) [(-1,- cos alpha),(cos alpha, 1)]`

`= 1/(sin^2 alpha)[(1,cos alpha),(- cos alpha, -1)]`

= `cosec^2 alpha [(1,cos alpha),(- cos alpha, -1)]`