C«ng thøc céng

cos(a–b) = cosa.cosb + sina.sinb cos(a+b) = cosa.cosb – sina.sinb sin(a–b) = sina.cosb – cosa.sinb sin(a+b) = sina.cosb + cosa.sinb

tan(a–b) = tan a−tan b

1+ tan a . tan b

tan(a+b) = tan a+ tan b

1−tan a . tan b

C«ng thøc nh©n ®«i

sin2a = 2sinacosa cos2a = cos2a – sin2a = 2 cos2a–1 = 1–2sin2a

tan2a = 2 tana

1−tan2

sin3a = 3sina – 4sin3a cos3a = 4cos3a – 3cosa

C«ng thøc biÕn ®æi tæng thµnh tÝch, tÝch thµnh tæng

cosacosb = 12

[cos(a–b) + cos(a+b)]

sinasinb = 12

[cos(a–b) – cos(a+b)]

sinacosb = 12

[sin(a–b) + sin(a+b)]

cosa + cosb = 2cos a+b

2cosa−b

2

cosa – cosb = –2sin a+b

2sina−b

2

sina + sinb = 2sin a+b

2cos

a−b2

sina – sinb = 2cos a+b

2sin

a−b2

tana ± tanb = sin(a±b)cosa. cosb

C«ng thøc h¹ bËc

sin2a = 1−cos2a

2

cos2a = 1+cos2a

2

C«ng thøc céng cos(a–b) = cosa.cosb

+ sina.sinb cos(a+b) = cosa.cosb

– sina.sinb sin(a–b) = sina.cosb –

cosa.sinb sin(a+b) = sina.cosb

+ cosa.sinb tan(a–b) =

tan a−tan b1+ tan a . tan b

tan(a+b) =

tan a+ tan b1−tan a . tan b

C«ng thøc h¹ bËc

sin2a = 1−cos2a

2

cos2a = 1+cos2a

2

tan2a = tan 2a−2tana

tan 2a

sin3a = 3 sina – sin 3a

4

cos3a = cos3a+3cosa

4Gi¸ trÞ lîng gi¸c cña c¸c gãc ®Æc biÖt:Cung bï nhau sin(π –α) = sinα cos(π –α) = – cosα tan(π –α) = – tanα cot(π –α) = – cotα

Cung h¬n kÐm π sin(π +α) = – sinα cos(π +α) = – cosα tan(π +α) = tanα cot(π +α) = cotα

Cung phô nhau

sin(π2

–α) = sinα

cos(π2

–α) = cosα

tan(π2

–α) = tanα

cot(π2

–α) = cotα

C«ng thøc biÕn ®æi tÝch thµnh tæng

cosacosb = 12

[cos(a–b) +

cos(a+b)]

sinasinb = 12

[cos(a–b) – cos(a+b)]

sinacosb = 12

[sin(a–b) + sin(a+b)]

C«ng thøc biÕn ®æi tæng thµnh tÝch

cosa + cosb = 2cosa+b

2cos

a−b2

cosa – cosb = –2sin a+b

2sina−b

2

sina + sinb = 2sina+b

2cos

a−b2

sina – sinb = 2cos a+b

2sin

a−b2

tana ± tanb = sin(a±b)cosa. cosb

C«ng thøc nh©n ®«i,nh©n ba sin2a = 2sinacosa cos2a = cos2a – sin2a = 2 cos2a–1

= 1–2sin2a

tan2a = 2 tana

1−tan2

sin3a = 3sina – 4sin3a cos3a = 4cos3a – 3cosa

tan3x = tanx(3−tan2 x)

1−3 tan2 x

Cung ®èi nhau cos(–α) = cosα sin(–α) = – sinα tan(–α) = – tanα cot(–α) = – cotα

Cung h¬n kÐm π2

sin(π2

+α) = – sinα

cos(π2

+α) = cosα

tan(π2

+α) = – tanα

cot(π2

+α) = – cotα