MathematicsIf ΔABC   is right angled at C, then the value of cos(A+B)   is

If ΔABC   is right angled at C, then the value of cos(A+B)   is


  1. A
         0
  2. B
         1
  3. C
        1 2  
  4. D
         3 2   

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    Solution:

    Given that ABC is right angled at C.
    According to the angle sum property of a triangle say ABC,   it can be represented as A+B+C= 180 °   Since ΔABC   is a right-angled triangle at C   means C= 90 °   .
    Substitute 90 °   for C   in A+B+C= 180 °   A+B+C= 180 °  
    A+B+ 90 ° = 180 ° A+B= 180 ° 90 ° A+B= 90 °   Take both sides cosine in the equation A+B= 90 °   .
    So,
    cos(A+B)=cos 90 °  
    We know that cos90° = 0.
    Therefore, cos(A+B)=0  .
    Therefore, option (1) is correct.
     
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