Question

prove that (tan teeetha +sec teetha-1)/(tan teetha-sec teetha+1)= 1+sin teetha/cos teetha​

Answer 1

Answer:

To Prove:

tanθ−secθ+1

tanθ+secθ−1

​

=  

cosθ

1+sinθ

​

 

Solution:

L.H.S =  

tanθ−secθ+1

tanθ+secθ−1

​

 

We can write, sec  

2

θ−tan  

2

θ=1

=  

tanθ−secθ+1

tanθ+secθ−(sec  

2

θ−tan  

2

θ)

​

 

=  

tanθ−secθ+1

tanθ+secθ−(secθ−tanθ)(secθ+tanθ)

​

 

=  

tanθ−secθ+1

(tanθ+secθ){1−(secθ−tanθ)}

​

 

=  

tanθ−secθ+1

(tanθ+secθ){1−secθ+tanθ}

​

 

=tanθ+secθ

=  

cosθ

sinθ

​

+  

cosθ

1

​

 

=  

cosθ

1+sinθ

​

 

= R.H.S

since L.H.S = R.H.S

tanθ−secθ+1

tanθ+secθ−1

​

=  

cosθ

1+sinθ

​

 

Hence Proved.