Double angle identities

Double angle identities are trigonometric identities that allow you to simplify expressions involving double the value of an angle. Some of the most commonly used double angle identities are:

• sin(2θ) = 2sin(θ)cos(θ)
• cos(2θ) = cos²(θ) – sin²(θ) = 2cos²(θ) – 1 = 1 – 2sin²(θ)
• tan(2θ) = (2tan(θ))/(1 – tan²(θ))

These identities can be used to find the sine, cosine, and tangent of double the value of an angle, and they are useful for solving problems involving complex trigonometry. They are based on the definitions of the sine and cosine functions and the Pythagorean identities for trigonometry.

Half angle identities are trigonometric identities that allow you to simplify expressions involving half the value of an angle. Some of the most commonly used half angle identities are:

• sin(θ/2) = ±√[(1 – cos(θ))/2]
• cos(θ/2) = ±√[(1 + cos(θ))/2]
• tan(θ/2) = ±√[(1 – cos(θ))/(1 + cos(θ))] = sin(θ)/(1 + cos(θ))

These identities can be used to find the sine, cosine, and tangent of half the value of an angle, and they are useful for solving problems involving complex trigonometry. They are based on the definitions of the sine and cosine functions and the Pythagorean identities for trigonometry.