sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa

cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb

tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)

cot(A+B)=(cotA cotB- 1)/(cot B+cotA)cot(A-B)=(cotA cotB+ 1)/(cot B-cotA)

Double angle formula

tan2A = 2 tana/( 1-tan2A)cot2A =(cot2A- 1)/2 cota

cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

sinα+sin(α+2π/n)+sin(α+2π* 2/n)+sin(α+2π* 3/n)+……+sin[α+2π*(n- 1)/n]= 0

Cos α+cos (α+2π/n)+cos (α+2π * 2/n)+cos (α+2π * 3/n)+…+cos [α+2π * (n-1)/n] = 0 and

sin^2(α)+sin^2(α-2π/3)+sin^2(α+2π/3)=3/2

tanAtanBtan(A+B)+tanA+tan B- tan(A+B)= 0

Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.

Cosine theorem b2=a2+c2-2accosB