MathematicsIf sin 77 ° =x,   then which of the following is the value of tan 77 °  ?

If sin 77 ° =x,   then which of the following is the value of tan 77 °  ?


  1. A
    1 1+ x 2  
  2. B
    x 1+ x 2  
  3. C
    x 1 x 2  
  4. D
    None of these 

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    Solution:

    The given trigonometric ratio is,
    sin 77 ° =x sin 2 77 ° = x 2  
    We know that,
    cos 2 x=1 sin 2 x cos 2 77 ° =1 sin 2 77 ° cos 2 77 ° =1 x 2 cos 77 ° = 1 x 2  
    Thus we have,
    tan 77 ° = sin 77 ° cos 77 ° tan 77 ° = x 1 x 2   Therefore, the value of tan 77 °  is x 1 x 2 .  
    Hence, option (3) is correct.
     
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