Question

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

1. `(1 + tan θ)/(1 + cot θ) = cot θ`
2. sec² θ − tan² θ = 1

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

Statement (i)

cot θ = `1/tan θ`

`(1 + tan θ)/(1 + 1/tan θ)`

`1 + 1/tan θ = (tan θ + 1)/tan θ`

= `(1 + tan θ)/((tan θ + 1)/tan θ)`

= `(1 + tan θ) xx tan θ/((1 + tan θ))`

= 1 × tan θ

= tan θ

Statement (ii)

It is one of the three fundamental Pythagorean Identities. It is derived by rearranging sec² θ = 1 + tan² θ

Subtracting tan² θ from both sides gives sec² θ − tan² θ = 1.