Question

sin+cos/sin-cos+sin-cos÷sin+cos=2sec^2÷tan^2-1

Answer 1

Hi, Here is your answer

Ans 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




OR


I assume the grouping is

 

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

I do not know what to do please help