Power Reducing Identities 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