Trigonometry Formulas Worksheet

The category based collection of Trigonometric formulas.
Trigonometry Identities
1. Sin2 θ + cos2 θ = 1
2. Sec2 θ - tan2 θ = 1
3. Cosec2 θ - cot2 θ = 1

Multiple Angle Identities
1. Sin 2A = 2 sin A . cos A
= 2 tan A / (1 + tan2 A)
2. Cos 2A = 1 - 2sin2 A
= 2cos2 A - 1
= (1 - tan2 A) / (1 + tan2 A)
3. tan 2A = (2 tan A) / (1 - tan2 A)
4. sin2 A = (1 - cos 2A) / 2
5. cos2 A = (1 + cos 2A) / 2
6. sin 3A = 3 sin A - 4 sin3 A
7. Cos 3A = 4 cos3 A - 3 cos A
8. tan 3A = (3 tan A - tan3 A) / (1 - 3 tan2 A)

Sub-multiple angle formula
1. sin A = 2 sin (A/2) cos (A/2)
= 2 tan (A/2) / (1 + tan2 (A/2) )
2. cos A = 1 - 2sin2 (A/2)
= 2cos2 (A/2) - 1
= (1 - tan2 (A/2)) / (1 + tan2 (A/2))
3. tan A = (2 tan (A/2)) / (1 - tan2 (A/2))

Half-angle Formula
1. sin (A/2) = √[(1 - cos A) / 2]
2. cos (A/2) = √[(1 + cos A) / 2]
3. tan (A/2) = √[(1 - cos A) / (1 + cos A)]

Product formula
1. sin C + sin D = 2 sin[(C + D) / 2]cos[(C - D) / 2]
2. sin C - sin D = 2 cos[(C + D) / 2]sin[(C - D) / 2]
3. cos C + cos D = 2 cos [(C + D) / 2]cos[(C - D) / 2]
4. cos C - cos D = - 2 sin [(C + D) / 2]sin[(C - D) / 2]

See also:
Trigonometry addition & subtraction formulas list.


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