Question

Prove that sec teta + tan teta + 1 /sec teta - tan teta +1 = 1 + sin teta/ cos teta.​

Answer 1

Answer:

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.