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Which sum or difference identity would you use to verify that cos (180° - q) = -cos q?
a. sin (a -b) = sin a cos b – cos a sin b
b. cos (a -b) = cos a cos b – sin a sin b
c. cos (a -b) = cos a cosb + sin a sin b
d. sin (a + b) = sin a cos b + cos a sin b

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Answer:

c. cos (a -b) = cos a cosb + sin a sin b

Step-by-step explanation:

The given identity is  [tex]\cos (180\degree-q)=-\cos q[/tex]

Using the formula: [tex]\cos (a-b)=\cos a\cos b+\sin a \sin b[/tex]

We put [tex]a=180\degree[/tex] and [tex]b=q[/tex] to get:

[tex]\cos (180\degree-q)=\cos 180\degree\cos q+\sin 180\degree \sin q[/tex]

[tex]\cos (180\degree-q)=-(1)\cos q+(0)\sin q[/tex]

[tex]\cos (180\degree-q)=-\cos q+0[/tex]

[tex]\cos (180\degree-q)=-\cos q[/tex]

The correct answer is C

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