A Level Pure Mathematics 3 (P3) – Comprehensive Revision Guide (Edexcel)

P2 - P3 Trigonometry Formulae
Standard Formulae
sin 𝑥
 tan 𝑥 = cos 𝑥
1
 sec 𝑥 = cos 𝑥
1
 cosec 𝑥 = sin 𝑥
1 cos 𝑥
 cot 𝑥 = tan 𝑥 = sin 𝑥

 𝑠𝑖𝑛2 𝑥 + 𝑐𝑜𝑠 2 𝑥 = 1
 𝑡𝑎𝑛2 𝑥 + 1 = 𝑠𝑒𝑐 2 𝑥
 1 + 𝑐𝑜𝑡 2 𝑥 = 𝑐𝑜𝑠𝑒𝑐 2 𝑥


Addition Formulae - Given

 sin(𝐴 ± 𝐵) = sin 𝐴 cos 𝐵 ± cos 𝐴 sin 𝐵
 cos(𝐴 ± 𝐵) = cos 𝐴 cos 𝐵 ∓ sin 𝐴 sin 𝐵
tan 𝐴±tan 𝐵
 tan(𝐴 ± 𝐵) = 1∓tan 𝐴 tan 𝐵


Double Angle Formulae
 sin 2𝐴 = 2 sin 𝐴 cos 𝐴
 cos 2𝐴 = 𝑐𝑜𝑠 2 𝐴 − 𝑠𝑖𝑛2 𝐴 = 2𝑐𝑜𝑠 2 𝐴 − 1 = 1 − 2𝑠𝑖𝑛2 𝐴
2 tan 𝐴
 tan 2𝐴 = 1−tan2 𝐴


Factor Formulae – Given
𝐴+𝐵 𝐴−𝐵
 sin 𝐴 + sin 𝐵 = 2 sin( ) cos( )
2 2
𝐴+𝐵 𝐴−𝐵
 sin 𝐴 − sin 𝐵 = 2 cos( ) sin( )
2 2
𝐴+𝐵 𝐴−𝐵
 cos 𝐴 + cos 𝐵 = 2 cos( ) cos( )
2 2
𝐴+𝐵 𝐴−𝐵
 cos 𝐴 − cos 𝐵 = 2 sin( ) sin( )
2 2