Question

The value of $ \sin^2 30^\circ + \cos^2 60^\circ $ is:

• A. \( \frac{1}{2} \)
• B. 1
• C. \( \frac{3}{4} \)
• D. \( \frac{1}{4} \)

Hint:

Remember the special angle values: \( \sin 30^\circ = \frac{1}{2} \), \( \cos 60^\circ = \frac{1}{2} \). Squaring and adding these values carefully helps in trigonometric computations.

Answer 1

The Correct Option is A

To find the value of \( \sin^2 30^\circ + \cos^2 60^\circ \), we first calculate each trigonometric function:  

\( \sin 30^\circ = \frac{1}{2} \) and \( \cos 60^\circ = \frac{1}{2} \).

Thus, \( \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \) and \( \cos^2 60^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \).

Adding these values gives \( \sin^2 30^\circ + \cos^2 60^\circ = \frac{1}{4} + \frac{1}{4} = \frac{1}{2} \).

Therefore, the correct answer is \( \frac{1}{2} \).

Answer 2

Step 1: Calculate \( \sin 30^\circ \) and \( \cos 60^\circ \). \[ \sin 30^\circ = \frac{1}{2}, \quad \cos 60^\circ = \frac{1}{2} \] Step 2: Square both values: \[ \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4}, \quad \cos^2 60^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \] Step 3: Add the squares: \[ \sin^2 30^\circ + \cos^2 60^\circ = \frac{1}{4} + \frac{1}{4} = \frac{1}{2} \] Hence, the value is \( \boxed{\frac{1}{2}} \).