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Revision:Trigonometry - Addition FormulaeTSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Trigonometry: Addition Formulae The results that must be learnt are:
Proof It can be shown that
By considering sin(A - B) = sin(A + (-B)):
By considering cos(A + B) = sin(π/2 - (A + B)) = sin((π/2 - A) - B):
By considering cos(A - B) = cos(A + (-B)):
It is immediately obvious that
which simplifies to the following identity when the numerator and denominator are divided by cos A and cos B:
Similarly,
We can derive the addition identities for cot in a similar way.
The addition identities for sec and csc are derived by taking the reciprocal of the identities for cos and sin, respectively, and multiplying the numerator and denominator by (sec A sec B csc A csc B).
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