Question

Value of $\sin^2\theta + \cos^2\theta$:

• A. 0
• B. 1
• C. 2
• D. -1

Hint:

No matter how complex the angle is (e.g., $\sin^2(5x+3) + \cos^2(5x+3)$), as long as the angles are identical, the result is always 1.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is the fundamental Pythagorean identity in trigonometry. It holds true for any real value of the angle $\theta$.
Step 2: Detailed Explanation:
In a right-angled triangle with sides $a, b$ and hypotenuse $c$: $\sin\theta = a/c$ and $\cos\theta = b/c$. $\sin^2\theta + \cos^2\theta = (a/c)^2 + (b/c)^2 = \frac{a^2 + b^2}{c^2}$. By Pythagoras theorem, $a^2 + b^2 = c^2$. So, $\frac{c^2}{c^2} = 1$.
Step 3: Final Answer:
The value is always 1.