MathematicsIf cos9α=sinα   and 9α< 90 ° ,   then which of the following is the value of tan5α  ?

If cos9α=sinα   and 9α< 90 ° ,   then which of the following is the value of tan5α  ?


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

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    Solution:

    The given equation is,
    cos9α=sinα   Apply the following:
    sinα=cos 90 ° α  
    Therefore we have,
    cos9α=cos 90 ° α 9α= 90 ° α 9α+α= 90 °  
    10α= 90 ° α= 90 ° 10 α= 9 °   Therefore,
    tan5α=tan5 9 ° tan5α=tan 45 ° tan5α=1   Therefore, the value of tan5α=1.   Hence, option (3) is correct.
     
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