Reciprocal relation: quotient relation: square relation:

tanα cotα= 1

sinα cscα= 1

cosαsecα= 1 sinα/cosα= tanα= secα/CSCα

cosα/sinα= cotα= CSCα/secαsin 2α+cos 2α= 1

1+tan2α=sec2α

1+cot2α=csc2α

sin(α+β)=sinαcosβ+cosαsinβ

sin(α-β)=sinαcosβ-cosαsinβ

cos(α+β)=cosαcosβ-sinαsinβ

cos(α-β)=cosαcosβ+sinαsinβ

tanα+tanβ

tan(α+β)=———

1-tanα tanβ

tanα-tanβ

tan(α-β)=———

1+tanα tanβ

2 tons (α/2)

sin2α=2sinαcosα

cos 2α= cos 2α-sin 2α= 2 cos 2α- 1 = 1-2 sin 2α

2tanα

tan2α=———

1-tan2α

sin3α=3sinα-4sin3α

cos3α=4cos3α-3cosα

3tanα-tan3α

tan3α=————

1-3tan2α

Sum and difference product formula of trigonometric function

α+β α-β