Question

In the following questions, two statements (i) and (ii) are given. Choose the valid statement.

(i) If `cot θ = a/b`, then `tan θ = b/a`.

(ii) sin θ · cot θ = cos θ.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

(i) `cot θ = a/b`

⇒ `tan θ = 1/(cot θ)`

= `1/(a/b)`

= `b/a`

Requires a, b ≠ 0.

(ii) sin θ · cot θ

= `sin θ · (cos θ/sin θ)` 

= cos θ 

Requires sin θ ≠ 0.

So, both identities hold wherever the expressions are defined.