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

The value of \( \sin^2 30^\circ + \cos^2 60^\circ \) is determined by calculating each term individually. We have \( \sin 30^\circ = \frac{1}{2} \) and \( \cos 60^\circ = \frac{1}{2} \). Squaring these gives \( \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \) and \( \cos^2 60^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \). The sum is \( \frac{1}{4} + \frac{1}{4} = \frac{1}{2} \). Consequently, the result is \( \frac{1}{2} \).