Question

prove that cot²+cosec²=cosec⁴-cot⁴​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

To Prove

→ cot²∅ + cosec²∅ = cosec⁴ - cot⁴

Proof

R.H.S → cosec⁴∅ - cot⁴∅

R.H.S → (cosec²∅)² - (cot²∅)²

R.H.S →(cosec²∅ + cot²∅)(cosec²∅ - cot²∅)

R.H.S →(1/sin²∅ + cos²∅/sin²∅)(1/sin²∅ - cos²∅/sin²∅)

R.H.S → (1 + cos²∅)/sin²∅ × (1 - cos²∅)/sin²∅

R.H.S →(1/sin²∅ + cos²∅/sin²) × sin²∅/sin²∅

R.H.S → cosec²∅ + cot²∅ = L.H.S

Hence Proved