Question

If sin θ + cos θ = 1, then the general value of θ is ______.

Options

• 2nπ

• `"n"π + (- 1)^"n" pi/4 - pi/4`

• `2"n"pi + pi/2`

• `("2n" - 1) + pi/4`

Answer 1

If sin θ + cos θ = 1, then the general value of θ is `underline("n"π + (- 1)^"n" pi/4 - pi/4)`.

Explanation:

sin θ + cos θ = 1

Dividing both sides by `sqrt(1^2 + 1^2) = sqrt2`, we get

`1/sqrt2 sin theta + 1/sqrt2 cos theta = 1/sqrt2`

`=> sin theta cos  pi/4 + cos theta  sin  pi/4 = 1/sqrt2`

`=> sin(theta + pi/4) = 1/sqrt2 = sin  pi/4`    ....[∴ sin (A + B) = sin A  cos B + cos A sin B]

`=> theta + pi/4 = "n"pi + (- 1)^"n" pi/4`

`=> theta = "n"pi + (- 1)^"n" pi/4 - pi/4`