Question

If $\tan 2A = 1$, where $2A$ is an acute angle, the value of $A$ will be:

• A. $36^\circ$
• B. $22\dfrac{1}{2}^\circ$
• C. $38^\circ$
• D. $45^\circ$

Hint:

When solving $\tan \theta = 1$, always remember the principal angle is $45^\circ$. Since $2A$ is acute, the only possible solution is $2A=45^\circ $\Rightarrow$ A=22.5^\circ$.

Answer 1

The Correct Option is B

Step 1: Given condition
\[ \tan 2A = 1 \]

Step 2: Recall standard tangent values
\[ \tan 45^\circ = 1 \]

Step 3: Equating angles
\[ 2A = 45^\circ \]

Step 4: Solve for $A$
\[ A = \frac{45^\circ}{2} = 22.5^\circ = 22\dfrac{1}{2}^\circ \] \[ \boxed{A = 22\dfrac{1}{2}^\circ} \]