Question

prove that tan prove that tan theta + sec theta minus one by tan theta minus sec theta + 1 is equal to 1 + sin theta by cos theta ​

Answer 1

Step-by-step explanation:

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