Question

If `2 sin 2θ = sqrt(2)`, then the value of θ is ______.

विकल्प

• 90°

• 60°

• 45°

• `(22 1/2)^circ`

Answer 1

If `2 sin 2θ = sqrt(2)`, then the value of θ is `underlinebb((22 1/2)^circ)`.

Explanation:

`2 sin 2θ = sqrt(2)` 

⇒ `sin 2θ = sqrt(2)/2`

⇒ sin 2θ = sin 45°

So, 2θ = 45° + 360°k or 2θ = 135° + 360°k, giving θ = 22.5° + 180°k or θ = 67.5° + 180°k.

Among the choices, 22.5° is listed, so `(22 1/2)^circ` is correct.