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Question
If A = B = 60°, verify that: cos(A - B) = cosA cosB + sinA sinB
Solution
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°
= `(1)/(2) xx (1)/(2) + sqrt(3)/(2) xx sqrt(3)/(2)`
= `(1)/(4) + (3)/(4)`
= `(4)/(4)`
= 1
L.H.S. = R.H.S.
Therefore,
cos(A - B) = cosA cosB + sinA sinB.
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