Question

If x = cosec 0 - cot 0, y = cosec 0 + cot O, find xy.​

Answer 1

We are given that x = cosec∅ - cot∅ and y = cosec∅ + cot∅.

Then, xy = (cosec∅ - cot∅)(cosec∅ + cot∅)

Since we know (a + b)(a - b) = a² - b².

→ cosec²∅ - cot²∅.

Now, cosec∅ = 1/ sin∅ and cot∅ = cos∅/sin∅

→ 1/sin²∅ - cos²∅/sin²∅

→ (1 - cos²∅)/sin²∅

By identity we know that 1 - cos²∅ = sin²∅.

→ sin²∅/sin²∅ = 1

Hence answer is 1.