The double angle formulas are:
\[ \sin(2θ) = 2\sin(θ)\cos(θ) \]
\[ \cos(2θ) = \cos^2(θ) - \sin^2(θ) \]
\[ \tan(2θ) = \frac{2\tan(θ)}{1 - \tan^2(θ)} \]
The term "double angle" refers to the expression of a trigonometric value of two times an angle θ. The double angle formulas allow you to calculate the trigonometric functions of twice the angle, which are different from simply doubling the trigonometric value of the original angle. These formulas are used in various fields of mathematics and physics to simplify complex trigonometric expressions and solve problems involving periodic functions.
Let's assume the following values:
Using the formula for sin(2θ):
\[ \sin(2 \times 45^\circ) = \sin(90^\circ) = 1 \]
The result is 1.
