Question

`(1 + tan θ)/(1 + cot θ)` is equal to ______.

Options

• sin θ

• cos θ

• tan θ

• cot θ

Answer 1

`(1 + tan θ)/(1 + cot θ)` is equal to tan θ.

Explanation:

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