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Question
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
Options
`[(-cos2x, sin2x),(-sin2x, cos2x)]`
`[(cos2x, -sin2x),(sin2x, cos2x)]`
`[(cos2x, sin2x),(sin2x, cos2x)]`
`[(tanx, 1),(-1, tanx)]`
MCQ
Fill in the Blanks
Solution
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = `[(cos2x, -sin2x),(sin2x, cos2x)]`.
Explanation:
AT = `[(1, tanx),(-tanx, 1)]`
A–1 = `([(1, - tanx),(tanx, 1)])/(1 + tan^2x)`
∴ AT A–1 = `1/(1 + tan^2x) [(1 - tan^2x, -2tanx),(2tanx, 1 - tan^2x)]`
= `[((1 - tan^2x)/(1 + tan^2x) (-2tanx)/(1 + tan^2x)),(((2tanx)/(1 + tan^2x), (1 - tan^2x)/(1 + tan^2x)))]`
= `[(cos2x, - sin2x),(sin2x, cos2x)]`
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