Question

show that cos /1-sin+sin/cos=2sec

Answer 1

cos/(1 + sin) + (1 + sin)/cos = 2 sec common denominator is cos(1 + sin)

[ cos · cos + (1 + sin)(1 + sin) ] / [cos(1 + sin)] = 2 sec

[ cos2 + sin2 + 2 sin + 1 ] / [cos(1 + sin)] = 2 sec

[ 1 + 2 sin + 1] / [cos(1 + sin)] = 2 sec

[ 2 sin + 2] / [cos(1 + sin)] = 2 sec

[ 2(sin + 1] / [cos(1 + sin)] = 2 sec

2 1/cos = 2 sec

2 sec = 2sec

Answer 2

Answer:

cos          (1+sin)  

(1+sin)  +     cos

 

=   cos2 + (1+sin)2  

        cos*(1+sin)

 

=   cos2 + 1 + 2sin + sin2  

          cos*(1+sin)

 

we know that cos2 + sin2 = 1

 

=    (1+1+2sin)  

     cos*(1+sin)  

 

=   (2+2sin)

   cos*(1+sin)

 

=      2(1+sin)

     cos*(1+sin)

 

=    2    

   cos  

 

=  2sec