Let tan(a/2)=t

sina=2t/( 1+t^2)

cosa=( 1-t^2)/( 1+t^2)

tana=2t/( 1-t^2)

2. Auxiliary angle formula

asint+bcost=(a^2+b^2)^( 1/2)sin(t+r)

cosr=a/[(a^2+b^2)^( 1/2)]

sinr=b/[(a^2+b^2)^( 1/2)]

tanr=b/a

3. Triple angle formula

sin(3a)=3sina-4(sina)^3

cos(3a)=4(cosa)^3-3cosa

tan(3a)=[3tana-(tana)^3]/[ 1-3(tana^2)]

4. Sum and difference of products

Sina * cosb =[sin(a+b)+sin(a-b)]/2

cosa * sinb =[sin(a+b)-sin(a-b)]/2

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

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

5. Sum and difference of products

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

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

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

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