# What is formula for Sin2x

## Trigonometric Identities and Formulas

Below are some of the most important definitions, identities and formulas in trigonometry.

1. ## Trigonometric Functions of Acute Angles

sin X = opp / hyp = a / c , csc X = hyp / opp = c / a
tan X = opp / adj = a / b , cot X = adj / opp = b / a
cos X = adj / hyp = b / c , sec X = hyp / adj = c / b ,
2. ## Trigonometric Functions of Arbitrary Angles

sin X = b / r , csc X = r / b
tan X = b / a , cot X = a / b
cos X = a / r , sec X = r / a
3. ## Special Triangles

Special triangles may be used to find trigonometric functions of special angles: 30, 45 and 60 degress.
4. ## Sine and Cosine Laws in Triangles

In any triangle we have:
1 - The sine law
sin A / a = sin B / b = sin C / c
2 - The cosine laws
a 2 = b 2 + c 2 - 2 b c cos A
b 2 = a 2 + c 2 - 2 a c cos B
c 2 = a 2 + b 2 - 2 a b cos C
5. ## Relations Between Trigonometric Functions

cscX = 1 / sinX
sinX = 1 / cscX
secX = 1 / cosX
cosX = 1 / secX
tanX = 1 / cotX
cotX = 1 / tanX
tanX = sinX / cosX
cotX = cosX / sinX
6. ## Pythagorean Identities

sin 2X + cos 2X = 1
1 + tan 2X = sec 2X
1 + cot 2X = csc 2X
7. ## Negative Angle Identities

sin(-X) = - sinX , odd function
csc(-X) = - cscX , odd function
cos(-X) = cosX , even function
sec(-X) = secX , even function
tan(-X) = - tanX , odd function
cot(-X) = - cotX , odd function
8. ## Cofunctions Identities

sin(π/2 - X) = cosX
cos(π/2 - X) = sinX
tan(π/2 - X) = cotX
cot(π/2 - X) = tanX
sec(π/2 - X) = cscX
csc(π/2 - X) = secX

cos(X + Y) = cosX cosY - sinX sinY
cos(X - Y) = cosX cosY + sinX sinY
sin(X + Y) = sinX cosY + cosX sinY
sin(X - Y) = sinX cosY - cosX sinY
tan(X + Y) = [ tanX + tanY ] / [ 1 - tanX tanY]
tan(X - Y) = [ tanX - tanY ] / [ 1 + tanX tanY]
cot(X + Y) = [ cotX cotY - 1 ] / [ cotX + cotY]
cot(X - Y) = [ cotX cotY + 1 ] / [ cotY - cotX]
10. ## Sum to Product Formulas

cosX + cosY = 2cos[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]
sinX + sinY = 2sin[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]
11. ## Difference to Product Formulas

cosX - cosY = - 2sin[ (X + Y) / 2 ] sin[ (X - Y) / 2 ]
sinX - sinY = 2cos[ (X + Y) / 2 ] sin[ (X - Y) / 2 ]
12. ## Product to Sum/Difference Formulas

cosX cosY = (1/2) [ cos (X - Y) + cos (X + Y) ]
sinX cosY = (1/2) [ sin (X + Y) + sin (X - Y) ]
cosX sinY = (1/2) [ sin (X + Y) - sin[ (X - Y) ]
sinX sinY = (1/2) [ cos (X - Y) - cos (X + Y) ]
13. ## Difference of Squares Formulas

sin 2X - sin 2Y = sin(X + Y)sin(X - Y)
cos 2X - cos 2Y = - sin(X + Y)sin(X - Y)
cos 2X - sin 2Y = cos(X + Y)cos(X - Y)
14. ## Double Angle Formulas

sin(2X) = 2 sinX cosX
cos(2X) = 1 - 2sin 2X = 2cos 2X - 1
tan(2X) = 2tanX / [ 1 - tan 2X ]
15. ## Multiple Angle Formulas

sin(3X) = 3sinX - 4sin 3X
cos(3X) = 4cos 3X - 3cosX
sin(4X) = 4sinXcosX - 8sin 3XcosX
cos(4X) = 8cos 4X - 8cos 2X + 1
16. ## Half Angle Formulas

sin (X/2) = + or - √ ( (1 - cosX) / 2 )
cos (X/2) = + or - √ ( (1 + cosX) / 2 )
tan (X/2) = + or - √ ( (1 - cosX) / (1 + cosX) )
= sinX / (1 + cosX) = (1 - cosX) / sinX
17. ## Power Reducing Formulas

sin 2X = 1/2 - (1/2)cos(2X))
cos 2X = 1/2 + (1/2)cos(2X))
sin 3X = (3/4)sinX - (1/4)sin(3X)
cos 3X = (3/4)cosX + (1/4)cos(3X)
sin 4X = (3/8) - (1/2)cos(2X) + (1/8)cos(4X)
cos 4X = (3/8) + (1/2)cos(2X) + (1/8)cos(4X)
sin 5X = (5/8)sinX - (5/16)sin(3X) + (1/16)sin(5X)