MathematicsIf tanα= 3  and tanβ= 1 3 ,   then which of the following is the value of the expression cot(α+β)  ?

If tanα= 3  and tanβ= 1 3 ,   then which of the following is the value of the expression cot(α+β)  ?


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

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    Solution:

    The given trigonometric ratio is,
    tanα= 3 tanα=tan 60 ° α= 60 °   Also,
    tanβ= 1 3 tanβ=tan 30 ° β= 30 °  
    Therefore we have,
    cot(α+β)=cot 60 ° + 30 ° cot(α+β)=cot 90 ° cot(α+β)=0  
    Therefore, the value of the expression cot(α+β)   is 0.
    Hence, option (1) is correct.
     
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