MathematicsA, Band Care interior angles of a triangle ABC. If A= 90 ° ,   then find the value of tan B+C 2  .

A, Band Care interior angles of a triangle ABC. If A= 90 ° ,   then find the value of tan B+C 2  .


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

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    Solution:

    Given that A, B and C are interior angles of a triangle ABC and A = 90°.
    We know that sum of interior angles of a triangle is 180 °  i.e. A+B+C= 180 °  .
    Then, B+C=180°A  ….(1)
    Given expression is tan B+C 2  .
    tan B+C 2 tan 180A 2 ....(from1) tan 180 2 A 2 tan 90 A 2  
    Using identity tan(90x)=cotx   .
     So, tan 90 A 2 =cot A 2   .
    Where, A= 90 °   cot A 2 cot 90 ° 2 cot 45 ° 1  
    Hence, the value of tan B+C 2 =1  .
    Therefore, option 1 is correct.
     
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