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2015-10-01T10:50:35+05:30

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LHS:
    [(sinФ+1)-cosФ][(sinФ+1)+cosФ]
=---------------------------------------------
   [(sinФ+cosФ)-1][(sinФ+cosФ)+1]
 
    (sinФ+1)² -cos²Ф
= ----------------------
   (sinФ+cosФ)²- 1²

     2 sin²Ф + 2 sinФ
= -----------------------
       2sinФcosФ
   
    sinФ +1
=------------
    cosФ
=tanФ+secФ
=secФ+tanФ
                         secФ-tanФ
=secФ+tanФ x ---------------
                        secФ -tanФ
     sec²Ф-tan²Ф  
= ------------------
     secФ-tanФ

=1/ secФ-tanФ                       [bcoz, sec²Ф-tan²Ф=1]
=RHS
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