Power reduction formula calculator uses the power reducing formulas to rewrite the expression.

Power reducing identity calculator** **is an online trigonometric identity calculator that calculates the value for trigonometric quantities with powers. It proficiently reduces the power of **sin**^{2}θ, cos^{2}θ, and **tan**^{2}θ and converts them to double angle.

Let’s find out formula of power reduction, and how to calculate power reducing trig function without using power reducing calculator.

## What is power reducing?

Power reducing is the process of evaluating the squared value of the three basic trigonometric functions (sin, cos, tan) using a reducing power function.

The power reduction formulas are obtained by solving the second and third versions of the cosine double-angle and half-angle formulas. In power reduction formulas, a trigonometric function is raised to a power such as:

**Sin2α or cos 2 α **

## How to reduce power of trigonometric identities?

To reduce the power of squared trig identities, follow the below steps:

**Example:**

Find the value of *sin*^{2}*θ,* *cos*^{2}*θ,* and *tan*^{2}θ, if the given angle is 30 degree.

**Solution:**

**Step 1: **Write down the angle.

*Θ = 30 *

**Step 2: **Place the angle value in the trig functions given above to calculate the value.

*sin*^{2}θ = [1 - cos (2θ)]/2

*sin*^{2} (30*°**) = [1 - cos (2(30**°**))]/2*

*sin*^{2} (30*°**) = [1 - cos (60**°**)]/2*

*sin*^{2} (30*°**) = [1 - cos (60**°**)]/2*

*sin*^{2} (30*°**) = (1 – 0.5)/2*

*sin*^{2} (30*°**) = 0.5/2*

*sin*^{2} (30*°**) = 0.25*

*cos*^{2}θ = [1 + cos (2θ)]/2

*cos*^{2 }*(30**°**) **= [1 + cos (2**(30**°**)**)]/2*

*cos*^{2 }*(30**°**) **= [1 + cos (6**0**°**)**]/2*

*cos*^{2 }*(30**°**) **= (1 + 0.5)/2*

*cos*^{2 }*(30**°**) **= 1.5/2*

*cos*^{2 }(30*°**) = 0.75*

*tan*^{2}θ = [1 - cos (2θ)]/ [1 + cos (2θ)]

*tan*^{2 }*(30**°**) **= [1 - cos (2**(30**°**)**]/ [1 + cos (2**(30**°**)**]*

*tan*^{2 }*(30**°**) **= [1 - cos **(60**°**)**]/ [1 + cos (6**0**°**)**]*

*tan*^{2 }*(30**°**) **= [1 – 0.5]/ [1 + 0.5]*

*tan*^{2 }*(30**°**) **= 0.5/ 1.5*

*tan*^{2 }(30*°**) = 0.33*

Power reduction calculator** **can perform all of the above calculations in blink of an eye. Moreover, you can use this tool to verify the outcomes of your manual calculations.