Question

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

Answer 1

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;

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

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

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

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

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