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Question

Choose the correct answer in the following question:

If A=[cosαsinαsinαcosα], then A+A'=I, if the value of α is

(a)π6(b)π3(c)π(d)3π2


Solution

Here, A=[cosαsinαsinαcosα]
and A=[cosαsinαsinαcosα]=[cosαsinαsinαcosα]
Given, A+A'=I
,[cosαsinαsinαcosα]+[cosαsinαsinαcosα]=[1001][2cosα002cosα]=[1001]
Comparing the corresponding elements of the above matrices, we have
2cosα=1cosα=12=cosπ3α=π3. So, correct option is (b).

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