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If t a n A = 1 x 2 + x + 1 , t a n B = x x 2 + x + 1 and t a n C = 1 x ( x 2 + x + 1 ) , then A + B =

Option 1 -

0

Option 2 -

π – C

Option 3 -

π 2 -C

Option 4 -

None

0 2 Views | Posted 4 weeks ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    4 weeks ago
    Correct Option - 3


    Detailed Solution:

    t a n B × t a n C = x x 2 + x + 1 × 1 x ( x 2 + x + 1 )

    = 1 x 2 + x + 1 = t a n 2 A            

    tan2 A = tan B tan C

    It is only possible when A = B = C at x = 1

    A = 30°, B = 30°, C = 30° [ t a n A = t a n B = t a n C = 1 3 ]                                 

    A + B = π 2 − C

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A
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