prove the following identity

Asked by  | 3rd May, 2008, 10:54: PM

Expert Answer:

  1+ cos A + sin A / 1 + cos A - sin A = 1 + sin A / cos A

    LHS

  1 + cos A + sin A / 1 + cos A - sin A

  (1 + cos A + sin A ) ( 1+ cos A + sin A)             ( 1 + cos2A + sin2A + 2 cos A + 2  cos A sin A + 2 sin A )

 ----------------------------------------------------   =      ---------------------------------------------------------------------------

   ( 1 + cos A )2  -  (sinA )2                                      1 + cos2A + 2 cos A - sin2A

    2+ 2 cos A + 2 cos A sin A + 2 sin A             2 ( 1 + cos A ) + 2 sin A ( 1 + cos A )            1 + sin A

  ---------------------------------------------------  =      -------------------------------------------------   =     --------------     RHS

  2 cos2A + 2 cos A                                                  2 cos A ( 1 + cos A )                                         cos A

Answered by  | 4th May, 2008, 12:13: AM

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