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We are tasked with finding the exact value of:

\[
\sin(151^\circ)\cos(91^\circ) - \cos(151^\circ)\sin(91^\circ)
\]

This expression is in the form of a trigonometric identity for the sine of a difference:

\[
\sin(A)\cos(B) - \cos(A)\sin(B) = \sin(A - B)
\]

In this case:

- \(A = 151^\circ\)
- \(B = 91^\circ\)

Thus, the expression simplifies to:

\[
\sin(151^\circ - 91^\circ) = \sin(60^\circ)
\]

The exact value of \(\sin(60^\circ)\) is:

\[
\sin(60^\circ) = \frac{\sqrt{3}}{2}
\]

Therefore, the exact value of the expression is:

\[
\boxed{\frac{\sqrt{3}}{2}}
\]

Would you like further explanation or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does the sine of the sum formula differ from the sine of the difference formula?
2. What are the exact values of other common angles like \(\sin(30^\circ)\), \(\sin(45^\circ)\), and \(\sin(90^\circ)\)?
3. Can you apply a similar formula for \(\cos(A)\cos(B) + \sin(A)\sin(B)\)?
4. How would the result change if the given angles were in radians instead of degrees?
5. What is the graphical interpretation of the sine and cosine functions at angles greater than \(90^\circ\)?

**Tip**: When working with trigonometric identities, recognizing standard forms like \(\sin(A - B)\) or \(\cos(A + B)\) can simplify your calculations significantly.

Use a sum or difference formula to find the exact value of the following: sin(151°)cos(91°) − cos(151°)sin(91°).

Learn how to find the exact value of sin(151°)cos(91°) − cos(151°)sin(91°) using the sine difference formula. This problem focuses on key trigonometric concepts and is suitable for students in Grades 9-12.

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