Q.

If  A=cos⁡θsin⁡θ−sin⁡θcos⁡θ,   then  A2=1 is true for

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a

θ=0

b

θ=π4

c

θ=π2

d

none of these

answer is A.

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Detailed Solution

We have, A2=cos⁡2θ    sin⁡2θ−sin⁡2θ    cos⁡2θ A2=I⇒cos⁡2θ=1  and  sin⁡2θ=0⇒θ=0
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If  A=cos⁡θsin⁡θ−sin⁡θcos⁡θ,   then  A2=1 is true for