Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which expression is equivalent to [tex]\cos \left(103^{\circ}\right) \cos \left(54^{\circ}\right) - \sin \left(103^{\circ}\right) \sin \left(54^{\circ}\right)[/tex]?

A. [tex]\sin \left(49^{\circ}\right)[/tex]
B. [tex]\cos \left(49^{\circ}\right)[/tex]
C. [tex]\sin \left(157^{\circ}\right)[/tex]
D. [tex]\cos \left(157^{\circ}\right)[/tex]

Sagot :

GinnyAnswer
To determine which expression is equivalent to [tex]\(\cos(103^\circ) \cos(54^\circ) - \sin(103^\circ) \sin(54^\circ)\)[/tex], we can use the angle addition formula for cosine. The angle addition formula states that:

[tex]\[ \cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B) \][/tex]

Given the expression [tex]\(\cos(103^\circ) \cos(54^\circ) - \sin(103^\circ) \sin(54^\circ)\)[/tex], we can recognize this as matching the form of [tex]\(\cos(A + B)\)[/tex] with [tex]\(A = 103^\circ\)[/tex] and [tex]\(B = 54^\circ\)[/tex]:

[tex]\[ \cos(103^\circ) \cos(54^\circ) - \sin(103^\circ) \sin(54^\circ) = \cos(103^\circ + 54^\circ) \][/tex]

Next, we add the angles:

[tex]\[ 103^\circ + 54^\circ = 157^\circ \][/tex]

Thus, the given expression simplifies to:

[tex]\[ \cos(157^\circ) \][/tex]

Therefore, the expression that is equivalent to [tex]\(\cos(103^\circ) \cos(54^\circ) - \sin(103^\circ) \sin(54^\circ)\)[/tex] is:

[tex]\[ \cos(157^\circ) \][/tex]

So the correct answer is:
[tex]\[ \cos(157^\circ) \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.