Power Reducing Identities 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 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 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 degree, find tan²θ.

Solution:

Step 1: Assign the given angle to θ.

θ = 45°

Step 2: Place the θ value in 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