MathematicsIf sinA= 1 2 ,  then the value of cotA is

If sinA= 1 2 ,  then the value of cotA is


  1. A
    3  
  2. B
    1 3  
  3. C
    3 2  
  4. D
    1 

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    Solution:

    Given that sinA= 1 2  .
    In a right-angle triangle say ABC  ,
    Pythagoras theorem is given by
    ( Hypotenuse ) 2 =(   Perpendicular ) 2 +(   Base ) 2   From the right-angle triangle, sinA   can be written as, sinA= BC AB   .
    Substitute 1 2   for sinA   in sinA= BC AB  .
    So,
    sinA= BC AB 1 2 = BC AB BC= 1 2 AB   From the right-angle triangle ABC,cotA   can be written as cotA= AC BC   .
    Substitute 1 2 AB   for BC   in cotA= AC BC   .
    So,
      cotA= AC BC cotA= AC 1 2 AB cotA= 2AC AB   From the Pythagoras theorem, in the right-angle triangle ABC  ,
    (AB) 2 = (AC) 2 + (BC) 2   Substitute 1 2 AB   for BC in (AB) 2 = (AC) 2 + (BC) 2  .
    (AB) 2 = (AC) 2 + (BC) 2 (AB) 2 = (AC) 2 + 1 2 AB 2 (AB) 2 = (AC) 2 + 1 4 (AB) 2   Solve further,
    1 1 4 (AB) 2 = (AC) 2 41 4 (AB) 2 = (AC) 2 3 4 (AB) 2 = (AC) 2 AC= 3 2 AB   Substitute 3 2 AB   for AC   in cotA= 2AC AB  .
    So,
    cotA= 2AC AB cotA= 2 3 2 AB AB cotA= 3   Therefore, the value of cosA= 3  .
    Therefore, option 1 is correct.
     
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