sinα+cosα=√2sin(α+π/4)

=√2[sinα(√2/2)+cosα(√2/2)]

=√2[sinαcos(π/4)+cosαsin(π/4)]

=√2sin(α+π/4)

公式asinx+bcosx=√(a²+b²)sin(x+φ)，tanφ=b/a

兩角和與差的三角函式 ：   

sin(a + b) = sin(a)cos(b) + cos(α)sin(b)  

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)    

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)  

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)    

tan(a + b) = [tan(a) + tan(b)] / [1 - tan(a)tan(b)]

tan(a - b) = [tan(a) - tan(b)] / [1 + tan(a)tan(b)]

和差化積公式 ：  

sin(a) + sin(b) = 2sin[(a + b)/2]cos[(a - b)/2]    

sin(a) - sin(b) = 2sin[(a - b)/2]cos[(a + b)/2]     

cos(a) + cos(b) = 2cos[(a + b)/2]cos[(a - b)/2]     

cos(a) - cos(b) = - 2sin[(a + b)/2]sin[(a - b)/2]     

積化和差公式 ：    

sin(a)sin(b) = - 1/2[cos(a + b) - cos(a - b)]    

cos(a)cos(b) = 1/2[cos(a + b) + cos(a -b)]    

sin(a)cos(b) = 1/2[sin(a + b) + sin(a - b)]   

二倍角公式 ：  

sin(2a) = 2sin(a)cos(a)     

cos 2a = cos2 a - sin2 a = 2cos2 a - 1= 1 - 2sin2 a