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Power Reducing Identities Calculator
Enter the angle in the below input field. Use the given buttons to find the power reduced trigonometric identities using power reducing formula calculator.
Power Reducing Formula Calculator
Power reducing identities calculator is an online trigonometric tool that is used to reduce the power of trigonometric identities. It is a bit tricky to find the value of squared, cubed, or fourth power trigonometric identities.
This power reducing calculator solves the following identities by using the power-reducing formula to rewrite the expression.
- Sin2x, Cos2x, Tan2x
- Sin3x, Cos3x, Tan3x
- Sin4x, Cos4x, Tan4x
Power reduction formulas
Power-reducing equations are given below.
sin2θ = [1 – cos (2θ)] / 2
cos2θ = [1 + cos (2θ)] / 2
tan2θ = [1 – cos (2θ)] / [1 + cos (2θ)]
These equations involve double angles to evaluate the square of trig identities.
Reducing the power of trigonometric identities
Let’s use an example to understand the process of reduction identities.
Example:
For an angle of 45 degrees, find tan2θ.
Solution:
Step 1: Assign the given angle to θ.
θ = 45°
Step 2: Place the θ value in the power reduction equation of tan2θ.
tan2θ = [1 - cos (2θ)]/ [1 + cos (2θ)]
tan2 (45°) = [1 - cos (2(45°)]/ [1 + cos (2(45°)]
tan2 (45°) = [1 - cos (90°)]/ [1 + cos (90°)]
tan2 (45°) = [1 – 0]/ [1 + 0]
tan2 (45°) = 1/ 1
tan2 (45°) = 1