Q.

If F(x)=cosxsinx0sinxcosx0001 and G(x)=cosx0sinx010sinx0cosx then [F(x).G(x)]-1

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a

{F(x)}-1{G(x)}-1

b

G(-x) F(-x)

c

F(x).G(x)

d

[G(x)]{f(x)}

answer is A.

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Detailed Solution

 (F(x).G(x))-1= G(x))-1(F(x))-1)
= G(-x).F(-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