Question

(1+cota_coseca)(1+tana+seca)=2 ​

Answer 1

Correct Question

Prove (1 + cotA - cosecA)(1 + tanA + secA) = 2.

Proof

(Given in attachment)

Procedure

1. Replace cotA by cosA/sinA and cosecA by 1/sinA. Similarly, tanA by sinA/cosA and secA by 1/cosA.

2. Take the L.C.M in second steps.

3. Group both bracket terms such that they match identity (a + b)(a - b) = a² - b². [Note: Here a = sinA + cosA]

4. Open brackets and remember that cos²A + sin²A = 1.

5. Similar terms will cancel and we will be left by 2.

→ L.H.S = R.H.S

Hence Proved