Question

sinA/cosA+1 = cosecA-cotA pls prove it​

Answer 1

To Prove

sinA/cosA+1 = cosecA-cotA

L.H.S → sinA/(cosA + 1)

Or sinA/(1 + cosA) _____(1)

By multiplying (1 - cosA) by (1),

→ sinA(1 - cosA)/(1 + cosA)(1 - cosA)

→ sinA(1 - cosA)/(1 - cos²A)

Since we know that,

• 1 - cos²A = sin²A

→ sinA(1 - cosA)/sin²A

→ 1/sinA - cosA/sinA

Since we know that,

• cosecA = 1/sinA
• cotA = cosA/sinA

→ cosecA - cotA = R.H.S

Hence Proved