Question

tanA + SecA - 1 / tanA - Sec A +1 = 1+ sinA / cosA​

Answer 1

Step-by-step explanation:

ANSWER

tanA−secA+1

tanA+secA−1

=

cosA

1+sinA

Taking L.H.S.-

tanA−secA+1

tanA+secA−1

=

tanA−secA+1

(tanA+secA)−(sec

2

A−tan

2

A)

[∵1+tan

2

A=sec

2

A]

=

tanA−secA+1

(tanA+secA)−(secA+tanA)(secA−tanA)

=

tanA−secA+1

(tanA+secA)(1−(secA−tanA))

=

tanA−secA+1

(tanA+secA)(1−secA+tanA)

=tanA+secA

=

cosA

sinA

+

cosA

1

=

cosA

1+sinA

= R.H.S.

Hence proved.