MathematicsIf sec2A=cosec A− 42 °  where 2A is an acute angle, then which of the following is the measure of the angle A?

If sec2A=cosec A 42 °  where 2A is an acute angle, then which of the following is the measure of the angle A?


  1. A
    32 °  
  2. B
    34 °  
  3. C
    36 °  
  4. D
    44 °   

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    Solution:

    The given equation is,
    sec2A=cosec A 42 °  
    Apply the following:
    cosec 90 ° θ =secθ  
    Therefore we have,
    cosec 90 ° 2A =cosec A 42 °  
    By comparing angles of sides, we obtain,
    90 ° 2A=A 42 ° 90 ° + 42 ° =A+2A 132 ° =3A A= 132 ° 3 A= 44 °   Therefore, the measure of the angle A= 44 ° .  
    Hence, option (4) is correct.
     
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