Question 1136438
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If sin(A) + cosec(A) = 2,  it means that


sin(A) + {{{1/sin(A)}}} = 2.


    A well known fact is that  x + {{{1/x}}} = 2  implies  x = 1.


Hence,  sin(A) = 1.


Then  {{{sin^5(A)}}} + {{{cosec^5(A)}}} = 1 + 1 = 2.       <U>ANSWER</U>
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Solved.