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

Step 1: Recall the basic identity.
For any angle, the squares of sine and cosine always add up to one.
\[ \sin^2\theta + \cos^2\theta = 1 \]

Step 2: Check with real values.
Here $\sin 30^\circ = \tfrac{1}{2}$ and $\cos 30^\circ = \tfrac{\sqrt{3}}{2}$.
\[ \left(\tfrac{1}{2}\right)^2 + \left(\tfrac{\sqrt{3}}{2}\right)^2 = \tfrac{1}{4} + \tfrac{3}{4} = 1 \]
So the value is one.
\[ \boxed{1} \]