Question

The general solution of cot θ + tan θ = 2 is ______.

Options

• θ = `("n"pi)/2 + (-1)^"n" pi/4`

• θ = `"n"pi + (-1)^"n" pi/8`

• θ = `("n"pi)/2 + (-1)^"n" pi/8`

• θ = `("n"pi)/2 + (-1)^"n" pi/6`

Answer 1

The general solution of cot θ + tan θ = 2 is θ = `("n"pi)/2 + (-1)^"n" pi/4`.

Explanation:

cot θ + tan θ = 2

∴ `1/tantheta + tan theta` = 2

⇒ 1 + tan²θ = 2 tan θ

∴ `(2tantheta)/(1 + tan^2theta)` = 1

⇒ sin 2θ = 1

⇒ 2θ = `"n"pi + (-1)^"n" pi/2`

⇒ θ = `("n"pi)/2 + (-1)^"n" pi/4`