Question

tanA + secA - 1 / tanA - secA + 1 = 1 + sinA / cosA

Answer 1

Answer:

To prove:

( tanA + secA -1)/( tanA- secA+1) = (1+sinA)/cosA

Proof:

(tanA - secA) - (sec^2A - tan^2A)/tanA + 1 - secA

(tanA - secA) (1 - (secA - tanA))/tanA + 1 - secA

(tanA - secA) (1 - secA + tanA)/tanA + 1 - secA

sec A + tan A

1/cosA + sinA/cosA

1 + sinA/cosA

Hence, Proved.

❤️Hope it will be helpful.❤️

Answer 2

Answer:

tan A + sec A - 1 1 + sin A

---------------------------- = ----------------

tan A - sec A +1 cos A

tan A + sec A - (1) 1 + sin A

---------------------------- = ----------------

tan A - sec A + (1) cos A

tan A + sec A - (

$\sec ^{2} (a)- tan {}^{2} ( a)$

)

----------------------------

tan A - sec A +1

tanA + secA - (secA-tanA)(secA+tanA)

-------------------------------------------------------------

tanA - secA + 1

tanA + secA ( 1 - sec A + tan A)

------------------------------------------------------

tan A - sec A +1

tan A + sec A

sin A + 1

--------- -----------

cos A cos A

1+sin A

--------------

cos A

LHS = RHS