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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.

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Formula

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

sin2θ = [1 - cos(2θ) ]2
cos2θ = [1 + cos(2θ) ]2
tan2θ = [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 sin2θ, cos2θ, and tan2θ 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 sin2θ, cos2θ, and tan2θ, 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.

  • sin2θ = [1 - cos (2θ)]/2

sin2 (30°) = [1 - cos (2(30°))]/2

sin2 (30°) = [1 - cos (60°)]/2

sin2 (30°) = [1 - cos (60°)]/2

sin2 (30°) = (1 – 0.5)/2

sin2 (30°) = 0.5/2

sin2 (30°) = 0.25

  • cos2θ = [1 + cos (2θ)]/2

cos2 (30°) = [1 + cos (2(30°))]/2

cos2 (30°) = [1 + cos (60°)]/2

cos2 (30°) = (1 + 0.5)/2

cos2 (30°) = 1.5/2

cos2 (30°) = 0.75

  • tan2θ = [1 - cos (2θ)]/ [1 + cos (2θ)]

tan2 (30°) = [1 - cos (2(30°)]/ [1 + cos (2(30°)]

tan2 (30°) = [1 - cos (60°)]/ [1 + cos (60°)]

tan2 (30°) = [1 – 0.5]/ [1 + 0.5]

tan2 (30°) = 0.5/ 1.5

tan2 (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.