TRIGO FORMULAE

sin(A+B)

sinAcosB+cosAsinB

sin(A-B)

sinAcosB-cosAsinB

cos(A+B)

cosAcosB-sinAsinB

cos(A-B)

cosAcosB+sinAsinB

2sinAcosB

sin(A+B)+sin(A-B)

2cosAsinB

sin(A+B)-sin(A-B)

2cosAcosB

cos(A+B)+cos(A-B)

2sinAsinB

cos(A-B)-cos(A+B)

sinC +sinD

2sin(C+D/2)cos(C-D/2)

sinC-sinD

2cos(C+D/2) sin(C-D/2)

cosC+cosD

2cos(C+D/2)cos(C-D/2)

cosC- cos D

2sin(C+D/2)sin(D-C/2)

sin(A+B)sin(A-B)

sin²A-sin²B

cos(A+B)cos(A-B)

cos²A - sin²B

sin75

√3 + 1 /2√2

cos15

√3 + 1 /2√2

cos75

√3 - 1 /2√2

sin15

√3 - 1 /2√2

tan75

2 +√3

cot15

2 +√3

cot75

2 -√3

tan15

2 -√3

sin18

√5 - 1 / 4

cos72

√5 - 1 / 4

cos36

√5 + 1 / 4

sin54

√5 + 1 / 4

tan(A+B)

tanA+tanB / 1-tanA.tanB

tan(A-B)

tanA-tanB / 1+tanA.tanB

1+tanθ/1-tanθ

tan(45+θ)

1-tanθ/1+tanθ

tan(45-θ)

cot(A+B)

cotA.cotB-1 / cotB+cotA

cot(A-B)

cotA.cotB+1 / cotB-cotA

sin(A+B+C)

sinA.cosB.cosC + sinB.cosA.cosC + sinC.cosA.cosB - sinA.sinB.sinC

cos(A+B+C)

cosA.cosB.cosC - cosA.sinB.sinC - cosB.sinA.sinC - cosC.sinA.sinB

tan(A+B+C)

tanA+tanB+tanC - tanA.tanB.tanC / 1- tanA.tanB -tanB.tanC - tanA.tanC

sin2θ

• 2sinθ.cosθ

• 2tanθ/1+tan²θ

cos2θ

• cos²θ-sin²θ

• 2cos²θ-1

• 1-2sin²θ

• 1-tan²θ / 1+tan²θ

1-cos2θ

2sin²θ

1+cos2θ

2cos²θ

tan2θ

2tanθ/1-tan²θ

sin3θ

3sinθ -4sin³θ

cos3θ

4cos³θ-3cosθ

tan3θ

3tanθ-tan³θ /1-3tan²θ

sinθ=sinα, θ=

nπ±(-1)ⁿα

cosθ=cosα, θ=

2nπ±α

tanθ=tanα, θ=

nπ+α

sin²θ=sin²α/ cos²θ=cos²α /tan²θ=tan²α atθ=

nπ±α

sinθ=0 at

nπ

cosθ=0 at

2nπ±π/2

tanθ=0

nπ

sinθ=1 at

2nπ-π/2

cosθ=1 at

2nπ

tanθ=1 at

2nπ+π/4

Tan(θ/2) (in terms of sin and cos)

(1-cosθ) /sinθ

tanA-tanB (in terms of son and cos)

sin(A-B) /cosA.cosB

CotA-cotB (in terms of sin and cos)

sin(B-A) /sinA.sinB

asinθ+bcosθ max and min value ( son and cos have same θ + both have power 1)

-root(a²+b²) to root(a²+b²)

sinθ. sin(60-θ). sin(60+θ)

¼ sin3θ

Cosθ. Cos(60-θ). Cos(60+θ)

¼ cos3θ

tanθ. Tan(60-θ). Tan(60+θ)

Tan3θ

cosθ. Cos2θ. Cos4θ… . n terms(each angle is doubling)

sin(2xlargest angle) /2ⁿsin(smallest angle)

sinθ+ sin(θ+a) +sin(θ+2a)… . Sin(θ+(n-1) a)

Cosθ+ cos(θ+a) +cos(θ+2a)… . Cos(θ+(n-1) a)