Question

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

1. `sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`
2. `sec θ = 1/cos θ`

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

Statement (i)

This is the fundamental Reciprocal Identity for secant. By definition, sec θ is the reciprocal of cos θ.

Statement (ii)

= `sqrt((1 + sin θ)/(1 - sin θ) xx (1 + sin θ)/(1 + sin θ))`

= `sqrt((1 + sin θ)^2/(1 - sin^2θ))`

= `sqrt((1 + sin θ)^2/(cos^2θ)`

= `(1 + sin θ)/cos θ`

= `1/cos θ + sin θ/cos θ`

= sec θ + tan θ