Power Reduction Formula
Squares 
Cubes 










Fourths 
Fifths 









Example: Find
Step 1: write sin^{4} x as a squared term
sin^{4} x = (sin^{2}x)^{2}
Step 2: use the squared power reduction rule for sine
Step 3: substitute using
Step 4: Simplify
Although the formula for the fourth power could have been used, it is much simpler to write the fourth power in terms of a squared power so that a double angle or half angle formula does not have to be used as well. Powerreducing formulas become very handy in calculus by allowing you to get rid of exponents in trigonometric functions in order to solve for an angle's measure.
Related Links: Math Trigonometry Product to Sum and Sum to Product Formulas Double Angle Identities 
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