Cosine of Sum/Mistake

Source Work

2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.):

compound angle formulae (in trigonometry)

Mistake

$\map \cos {a \pm b} = \cos a \cos b \pm \sin a \sin b$

Correction

This should read:

$\map \cos {a \pm b} = \cos a \cos b \mp \sin a \sin b$

Otherwise it would be interpreted as:

$\map \cos {a + b} = \cos a \cos b + \sin a \sin b$

$\map \cos {a - b} = \cos a \cos b - \sin a \sin b$

which is incorrect.

The correct identities are:

$\map \cos {a + b} = \cos a \cos b - \sin a \sin b$

$\map \cos {a - b} = \cos a \cos b + \sin a \sin b$

In the $6$th edition, the structure of the dictionary has changed to put these formulae into an appendix where they are specified in full, error-free.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): compound angle formulae (in trigonometry)