Question

If sin 2x = 2 sin 45° cos 45°; the value of x is ______.

Options

• 45°

• 90°

• 30°

• 60°

Answer 1

If sin 2x = 2 sin 45° cos 45°; the value of x is 45°.

Explanation:

Solving,

⇒ sin 2x = 2 sin 45° cos 45°

\[\Rightarrow \sin 2x = 2 \times \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}}\]

\[\Rightarrow \sin 2x = 2 \times \frac{1}{2}\]

⇒ sin 2x = 1

⇒ sin 2x = sin 90°

⇒ 2x = 90°

\[\Rightarrow x = \frac{90^\circ}{2} = 45^\circ\]