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  • Let A= theta : 2cos ^2 theta +sin theta less than equal to 2 and B = theta : pi/2 less than equal to ( theta) less than equal to 3pi/2 Find A intersection B=?

Let A= theta : 2cos ^2 theta +sin theta less than equal to 2 and B = theta : pi/2 less than equal to ( theta) less than equal to 3pi/2 Find A intersection B=?

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Solution:    

              \A=\theta :2-2sin^2 heta +sin heta leq 2\ \=\theta :sin heta (1-2sin heta )leq 0

     Above is possible if  sin heta leq 0   or  sin heta geq frac12

   sin heta =frac12   when heta =fracpi 6  and is greater than half frac12

   When    fracpi 6leq heta leq frac5pi 6

   Also    sin heta leq 0  where pi leq heta leq 2pi .

  herefore     A=\theta :fracpi 6leq frac5pi 6 hspace0.2cmor hspace0.2cmpi leq heta leq 2pi

        B=\theta :fracpi 2leq heta leq frac3pi 2

  herefore    Acap B=\theta :fracpi2leq heta leq frac5pi6 hspace0.2cmor hspace0.2cmpileq heta leq 2pi 

Posted by

Deependra Verma

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