MathematicsWhich of the following is the value of the expression 3sin 43 ° cos 47 ° 2 − cos 37 ° cosec 53 ° tan 5 ° tan 25 ° tan 45 ° tan 65 ° tan 85 °  ?

Which of the following is the value of the expression 3sin 43 ° cos 47 ° 2 cos 37 ° cosec 53 ° tan 5 ° tan 25 ° tan 45 ° tan 65 ° tan 85 °  ?


  1. A
    2
  2. B
    4
  3. C
    6
  4. D
    8 

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    Solution:

    The given expression is,
    3sin 43 ° cos 47 ° 2 cos 37 ° cosec 53 ° tan5tan 25 ° tan 45 ° tan 65 ° tan 85 °   Apply the following:
    cosecθ= 1 sinθ  
    3sin 43 ° cos (9043) ° 2 cos (9053) ° × 1 sin 53 ° tan 5 ° tan 25 ° tan 45 ° tan (9025) ° tan (905) °   Apply the following:
    cos 90 ° θ =sinθ, tan 90 ° θ =cotθ  
    Therefore we have,
    3sin 43 ° sin 43 ° 2 sin 53 ° × 1 sin 53 ° tan 5 ° tan 25 ° (1)cot 25 ° cot 5 °  
    (3) 2 1 tan 5 ° ×tan 25 ° × 1 tan 25 ° × 1 tan 5 °  
    (9) 1 1 8  
    Therefore, the value of the expression 3sin 43 ° cos 47 ° 2 cos 37 ° cosec 53 ° tan 5 ° tan 25 ° tan 45 ° tan 65 ° tan 85 ° =8.  
    Hence, option (4) is correct.
     
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