Question

If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.

Options

• `"b"/"a"`

• `"a"/"b"`

• ab

• a – b

Answer 1

If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to `"a"/"b"`.

Explanation:

`(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`

By componendo – dividendo, we get

`(cos(x - y) + cos(x + y))/(cos(x - y) - cos(x + y)) = (("a" + "b") + ("a" - "b"))/(("a" + "b") - ("a" - "b"))`

⇒ `(2cos x cosy)/(2sinx siny) = (2"a")/(2"b")`

⇒ cot x × cot y = `"a"/"b"`