Question

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

1. `cot θ = sin θ/cos θ`
2. `1/(tan θ + cot θ) = sin^2 θ . cos^2 θ`

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Neither (i) nor (ii)

Explanation:

Statement (i)

By definition, `tan θ = sin θ/cos θ`. The cotangent function is the reciprocal of the tangent, which means `cot θ =  cos θ/sin θ`

Statement (ii)

LHS = `1/(sin θ/cos θ + cos θ/sin θ)`

= `1/((sin^2 θ + cos^2 θ)/(cos θ.sin θ))`

= `1/(1/(cos θ.sin θ))`

= sin θ.cos θ