The formulas to calculate the power reduction of an angle (θ) are:
\[ \sin^2(\theta) = \frac{1 - \cos(2\theta)}{2} \]
\[ \cos^2(\theta) = \frac{1 + \cos(2\theta)}{2} \]
\[ \tan^2(\theta) = \frac{1 - \cos(2\theta)}{1 + \cos(2\theta)} \]
Power reducing is the process of calculating the squared value of the three trigonometric functions using a reducing power function, as shown above. These formulas are useful in various fields of mathematics and engineering to simplify expressions and solve problems involving trigonometric functions.
Let's assume the angle (θ) is 45 degrees:
Using the formulas to calculate the power reduction:
\[ \sin^2(45^\circ) = \frac{1 - \cos(90^\circ)}{2} = \frac{1 - 0}{2} = 0.5 \]
\[ \cos^2(45^\circ) = \frac{1 + \cos(90^\circ)}{2} = \frac{1 + 0}{2} = 0.5 \]
\[ \tan^2(45^\circ) = \frac{1 - \cos(90^\circ)}{1 + \cos(90^\circ)} = \frac{1 - 0}{1 + 0} = 1 \]
The results are \(\sin^2(45^\circ) = 0.5\), \(\cos^2(45^\circ) = 0.5\), and \(\tan^2(45^\circ) = 1\).
