FURTHER PURE MATHEMATICS FP2
FACTORISATION FORMULAE
SUMMARY
sin sin 2sin cos
22
sin sin 2cos sin
22
cos cos 2cos cos
22
cos cos 2sin sin
22
AB AB
AB
AB AB
AB
AB AB
AB
AB AB
AB
+
−
+=
+−
−=
+
−
+=
+
−
−=−
These formulae may be remembered as:
Sum of two sines= 2sin(semi sum)cos(semi difference)
Difference of two sines= 2cos(semi sum)sin(semi difference)
Sum of two cosines= 2 cos(semi sum)cos(semi difference)
Difference of two cosines= minus 2 sin(semi sum)sin(semi
difference)
They are however given in the formula booklet.
They are used to FACTORISE trigonometric equations involving sin and cos.
This means writing a SUM or DIFFERENCE as a PRODUCT.
The main use will be to solve equations involving sums or differences of sin and
cos which can be arranged to equal zero.
