Question

Prove that tan theta + sec theta - 1 / tan theta - sec theta + 1 = 1+ sin theta / cos theta

Answer 1

Answer:

Hey mate, Kindly refer to the attachment.

Hope it helps you✌

Sorry for rough handwriting.

Answer 2

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.