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$If F (x) = [\begin{array}{ccc} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{array}] and G (x) [\begin{array}{ccc} \cos x & 0 & \sin x \\ 0 & 1 & 0 \\ - \sin x & 0 & \cos x \end{array}] then [F (x) G (x)]^{- 1} =$

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F−xG−x

Fx−1Gx−1

G−xF−x

Gx−1Fx−1

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detailed solution

Correct option is C

F(x) and G(x) has the property that (F(x))−1=F(−x) and (G(x))−1=G(−x)FxGx−1=Gx−1Fx−1 =G−xF−x

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If F(x)=cos⁡x−sin⁡x0sin⁡xcos⁡x0001 and G(x)cos⁡x0sin⁡x010−sin⁡x0cos⁡x then [F(x)G(x)]−1=

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$If F (x) = [\begin{array}{ccc} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{array}] and G (x) [\begin{array}{ccc} \cos x & 0 & \sin x \\ 0 & 1 & 0 \\ - \sin x & 0 & \cos x \end{array}] then [F (x) G (x)]^{- 1} =$