Question

Find the value of sin²25°+sin²65°.

• A. 0
• B. 1
• C. -1
• D. \( \frac{1}{\sqrt 2} \)
• E. None of these

Answer 1

The Correct Option is A

Step 1: Understand the given expression.
We are asked to find the value of:
\( \sin^2 25^\circ + \sin^2 65^\circ \)

Step 2: Use a trigonometric identity.
We can use the identity: \( \sin(90^\circ - x) = \cos(x) \). This gives:
\( \sin 65^\circ = \cos 25^\circ \).
So, we can rewrite the expression as:
\( \sin^2 25^\circ + \sin^2 65^\circ = \sin^2 25^\circ + \cos^2 25^\circ \)

Step 3: Apply the Pythagorean identity.
According to the Pythagorean identity, \( \sin^2 x + \cos^2 x = 1 \). Therefore:
\( \sin^2 25^\circ + \cos^2 25^\circ = 1 \).

Step 4: Conclusion.
The value of \( \sin^2 25^\circ + \sin^2 65^\circ \) is 1.

Final Answer:
The correct option is (A): 0.