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# Power Reducing Formula Calculator

Enter the angle in degree and press the buttons below to get the power reduced trigonometric identities using power reducing identities calculator.

Table of Contents:

## Formula

The below equations use cosine double angle and half angle to reduce the power of squared trigonometric identities.

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

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**and converts them to double angle.

^{2}θLet’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}**and**

*θ,***if the given angle is 30 degree.**

*tan*^{2}θ,**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.