GrandMaster87 said:
njama said:By multiplying [itex]\frac{sin3x}{sinx}[/itex] with [itex]\frac{cos(x)}{cos(x)}[/itex] and [itex]\frac{cos(3x)}{cos(x)}[/itex] with [itex]\frac{sin(x)}{sin(x)}[/itex] you got:
[tex]\frac{cos(x)sin(3x)-sin(x)cos(3x)}{sin(x)cos(x)}[/tex]
What can you spot now?
GrandMaster87 said:
GrandMaster87 said:
Trignometric identities are mathematical equations that involve trigonometric functions, such as sine, cosine, and tangent, and are true for all values of the variables involved. They are used to simplify and manipulate trigonometric expressions.
There are three main types of trignometric identities: Pythagorean identities, reciprocal identities, and quotient identities. Each type has multiple variations and can be used to solve different types of problems.
The Pythagorean identity is a trignometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent. It states that sin²θ + cos²θ = 1, and can be used to solve problems involving right triangles.
Trignometric identities have many real-life applications in fields such as engineering, physics, and astronomy. They can be used to solve problems involving angles, distances, and other geometric concepts.
One common mistake when using trignometric identities is forgetting to check the domain of the function. Trignometric identities are only valid for certain values of the variables, so it is important to make sure that the values being used fall within the domain of the function.