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3 years ago

Find the exact value of the expression. Sin 265 cos 25 - cos 265 sin 25

1 answer:

4 0

Answer:

$\sin(265\degree) \cos(25\degree)-\sin(265\degree) \cos(25\degree)=-\frac{\sqrt{3}}{2}$

Step-by-step explanation:

Recall that;

$\sin(A) \cos(B)-\sin(B) \cos(A)=\sin(A-B)$

This implies that;

$\sin(265\degree) \cos(25\degree)-\sin(265\degree) \cos(25\degree)=\sin(265\degree-25\degree)$

$\sin(265\degree) \cos(25\degree)-\sin(265\degree) \cos(25\degree)=\sin(240\degree)$

$\sin(265\degree) \cos(25\degree)-\sin(265\degree) \cos(25\degree)=\sin(180\degree+60\degree)$

$\sin(265\degree) \cos(25\degree)-\sin(265\degree) \cos(25\degree)=-\sin(60\degree)$

$\sin(265\degree) \cos(25\degree)-\sin(265\degree) \cos(25\degree)=-\frac{\sqrt{3}}{2}$

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