Question

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

Answer 1

Answer: Choice C

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

In this case, we'd have a = 180 and b = q, so,

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

cos(180 - q) = cos(180)cos(q) + sin(180)sin(q)

cos(180 - q) = -1*cos(q) + 0*sin(q)

cos(180 - q) = -cos(q) + 0

cos(180 - q) = -cos(q)