Question

If A = B = 60°, verify that: cos(A - B) = cosA cosB + sinA sinB

Answer 1

cos(A - B) = cosA cosB + sinA sinB
L.H.S. :
cos(60° - 60°) = cos0° = 1
R.H.S. :
cosA cosB + sinA sinB
= cos60° cos60° + sin60° sin60°

= ${\displaystyle \frac{1}{2}\times \frac{1}{2}+\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}}$

= ${\displaystyle \frac{1}{4}+\frac{3}{4}}$

= ${\displaystyle \frac{4}{4}}$
= 1
L.H.S. = R.H.S.
Therefore,
cos(A - B) = cosA cosB + sinA sinB.