Question

The value of \(\sin^2 30^\circ + \cos^2 30^\circ\) is: 

• A. 1
• B. 0
• C. 0.5
• D. \(\sqrt{3}\) Correct Answer: (A) 1 Solution:

Hint:

Always remember the identity: \[ \sin^2\theta+\cos^2\theta=1 \] It is one of the most frequently used formulas in trigonometry.

Answer 1

The Correct Option is A

Concept: One of the fundamental identities in trigonometry is the Pythagorean identity: \[ \sin^2\theta + \cos^2\theta = 1 \] This identity is true for every value of \(\theta\).

Step 1: Substitute \(\theta = 30^\circ\). Using the identity directly, \[ \sin^2 30^\circ + \cos^2 30^\circ = 1 \] Thus the answer is immediately obtained.

Step 2: Verify using standard trigonometric values. We know that \[ \sin 30^\circ = \frac{1}{2} \] and \[ \cos 30^\circ = \frac{\sqrt{3}}{2} \] Therefore, \[ \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \] and \[ \cos^2 30^\circ = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3}{4} \] Adding them, \[ \frac{1}{4}+\frac{3}{4} = \frac{4}{4} = 1 \]

Step 3: State the final result. \[ \boxed{\sin^2 30^\circ+\cos^2 30^\circ = 1} \] Hence, the correct option is \(\boxed{(A)}\).