Question

important formulae of chapter trigonometric functions class 11 ?

Answer 1

Trigonometry Class 11 Formulas

sin(−θ)=−sinθ

sin(−θ)=−sinθ

cos(−θ)=cosθ

cos(−θ)=cosθ

tan(−θ)=−tanθ

tan(−θ)=−tanθ

cosec(−θ)=−cosecθ

cosec(−θ)=−cosecθ

sec(−θ)=secθ

sec(−θ)=secθ

cot(−θ)=−cotθ

cot(−θ)=−cotθ

Product to Sum Formulas

sinx siny=

1

2

[cos(x–y)−cos(x+y)]

sinx siny=12[cos(x–y)−cos(x+y)]

cosxcosy=

1

2

[cos(x–y)+cos(x+y)]

cosxcosy=12[cos(x–y)+cos(x+y)]

sinxcosy=

1

2

[sin(x+y)+sin(x−y)]

sinxcosy=12[sin(x+y)+sin(x−y)]

cosxsiny=

1

2

[sin(x+y)–sin(x−y)]

cosxsiny=12[sin(x+y)–sin(x−y)]

Sum to Product Formulas

sinx+siny=2sin(

x+y

2

)cos(

x−y

2

)

sinx+siny=2sin(x+y2)cos(x−y2)

sinx−siny=2cos(

x+y

2

)sin(

x−y

2

)

sinx−siny=2cos(x+y2)sin(x−y2)

cosx+cosy=2cos(

x+y

2

)cos(

x−y

2

)

cosx+cosy=2cos(x+y2)cos(x−y2)

cosx−cosy=–2sin(

x+y

2

)sin(

x−y

2

)

cosx−cosy=–2sin(x+y2)sin(x−y2)

Basic Formulas

sin(A+B)=sinAcosB+cosAsinB

sin(A+B)=sinAcosB+cosAsinB

sin(A−B)=sinAcosB–cosAsinB

sin(A−B)=sinAcosB–cosAsinB

cos(A+B)=cosAcosB–sinAsinB

cos(A+B)=cosAcosB–sinAsinB

cos(A–B)=cosAcosB+sinAsinB

cos(A–B)=cosAcosB+sinAsinB

tan(A+B)=

tanA+tanB

1–tanAtanB

tan(A+B)=tanA+tanB1–tanAtanB

tan(A–B)=

tanA–tanB

1+tanAtanB

tan(A–B)=tanA–tanB1+tanAtanB

cos(A+B)cos(A–B)=

cos

2

A–

sin

2

B=

cos

2

B–

sin

2

A

cos(A+B)cos(A–B)=cos2A–sin2B=cos2B–sin2A

sin(A+B)sin(A–B)=

sin

2

A–

sin

2

B=

cos

2

B–

cos

2

A

sin(A+B)sin(A–B)=sin2A–sin2B=cos2B–cos2A

sin2A=2sinAcosA=

2tanA

1+

tan

2

A

sin2A=2sinAcosA=2tanA1+tan2A

cos2A=

cos

A

–

sin

2

A=1–2si

n

2

A=2co

s

2

A–1=

1−

tan

2

A

1+

tan

2

A

cos2A=cosA–sin2A=1–2sin2A=2cos2A–1=1−tan2A1+tan2A

tan2A=

2tanA

1–

tan

2

A

tan2A=2tanA1–tan2A

\sin 3A = 3\sin A – 4\sin^{3}A = 4\sin\left(60^{\circ}-A).\sin A .\sin\left( 60^{\circ}+A \right )

\sin 3A = 3\sin A – 4\sin^{3}A = 4\sin\left(60^{\circ}-A).\sin A .\sin\left( 60^{\circ}+A \right )

cos3A=4

cos

3

A–3cosA=4cos(

60

∘

−A).cosA.cos(

60

∘

+A)

cos3A=4cos3A–3cosA=4cos(60∘−A).cosA.cos(60∘+A)

tan3A=

3tanA–

tan

3

A

1−3

tan

2

A

=tan(

60

∘

−A).tanA.tan(

60

∘

+A)

tan3A=3tanA–tan3A1−3tan2A=tan(60∘−A).tanA.tan(60∘+A)

sinA+sinB=2sin

A+B

2

cos

A−B

2

sinA+sinB=2sinA+B2cosA−B2