Question

If $\sin A = \cos A$, then the value of $A$ will be:

• A. $0^\circ$
• B. $30^\circ$
• C. $45^\circ$
• D. $60^\circ$

Hint:

Whenever $\sin \theta = \cos \theta$, the angle $\theta$ is always $45^\circ$ (or $\pi/4$ radians).

Answer 1

The Correct Option is C

Step 1: Given condition.
It is given that $\sin A = \cos A$.

Step 2: Divide both sides by $\cos A$.
\[ \frac{\sin A}{\cos A} = 1 \] \[ \tan A = 1 \]
Step 3: Recall the trigonometric ratio.
The value of $A$ for which $\tan A = 1$ is: \[ A = 45^\circ \]
Step 4: Verification.
At $A = 45^\circ$, \[ \sin 45^\circ = \cos 45^\circ = \frac{1}{\sqrt{2}}, \] which satisfies the given condition.

Step 5: Conclusion.
Hence, the value of $A$ is $45^\circ$.