Question

\(\sin 2 \theta = 2 \sin \theta\) is true, when \(\theta\) is equal to

• A. 90\(^\circ\)
• B. 60\(^\circ\)
• C. 45\(^\circ\)
• D. 0\(^\circ\)

Hint:

An easy way is to test Option (D) directly:
LHS = \(\sin (2 \times 0^\circ) = \sin 0^\circ = 0\)
RHS = \(2 \sin 0^\circ = 2(0) = 0\)
Since LHS = RHS, \(0^\circ\) is correct!

Answer 1

The Correct Option is D

Step 1: Recall the equation.
We need $\sin 2\theta = 2\sin\theta$ to hold for one of the given standard angles.
Step 2: Test each option directly instead of solving algebraically.
$\theta=90^\circ$: $\sin 180^\circ = 0$, but $2\sin 90^\circ = 2$, not equal. $\theta=60^\circ$: $\sin 120^\circ \approx 0.87$, but $2\sin 60^\circ \approx 1.73$, not equal. $\theta=45^\circ$: $\sin 90^\circ = 1$, but $2\sin 45^\circ \approx 1.41$, not equal.
Step 3: Confirm the match.
$\theta=0^\circ$: $\sin 0^\circ = 0$ and $2\sin 0^\circ = 0$, both sides equal.
\[ \boxed{\theta = 0^\circ} \]