Question

simplify

cot^2A (secA-1)/1+sinA
​

Answer 1

We have to find the final outcome of cot²A(secA - 1)/(1 + sinA)

Before solving remember that:

• sin²A = 1 - cos²A
• 1 - cos²A = (1 + cosA)(1 - cosA)
• cotA = cosA/sinA

→ cot²A(secA - 1)/(1 + sinA)

Let's solve numerator first

→ cot²(secA - 1)

→ cos²A/sin²A × (1/cosA - 1)

→ cos²A/sin²A × (1 - cosA)/cosA

→ cosA(1 - cosA)/sin²A

Bringing numerator and denominator together

→ cos(1 - cosA)/sin²A(1 + sinA)

→ cos(1 - cosA)/(1 - cos²A)(1 + sinA)

→ cos(1 - cosA)/(1 - cosA)(1 + cosA)(1 + sinA)

→ cosA/(1 + cosA)(1 + sinA)

Hence final outcome is cosA/(1 + cosA)(1 + sinA).