To simplify \(\sin^2(270^\circ - A)\):

1. Start by recognizing the identity for \(\sin(270^\circ - A)\). This is related to the sine function's behavior under transformations:

\[
\sin(270^\circ - A) = -\cos(A)
\]

2. Now, square the expression:

\[
\sin^2(270^\circ - A) = (-\cos(A))^2
\]

3. Since the square of \(-\cos(A)\) is just \(\cos^2(A)\):

\[
\sin^2(270^\circ - A) = \cos^2(A)
\]

So, \(\sin^2(270^\circ - A) = \cos^2(A)\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How does the sine function behave under transformations like \( \sin(180^\circ - A) \)?
2. What is the general formula for \( \sin^2(x) + \cos^2(x) \)?
3. Can you explain the trigonometric identity for \( \cos(90^\circ + A) \)?
4. How does the Pythagorean identity relate to \(\sin^2(x)\) and \(\cos^2(x)\)?
5. What is the difference between \(\sin^2(A)\) and \((\sin(A))^2\)?

**Tip:** When simplifying trigonometric expressions, always look for standard identities or transformations involving key angles like \(90^\circ\), \(180^\circ\), and \(270^\circ\).

Explore the solution for Sin²(270° - A) using trigonometric identities. This problem covers angle transformations and the relationship between sine and cosine functions. Suitable for students in Grades 9-12.

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