what are the power reducing identities for trig?

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Start with the identities for `cos2theta` :

(a) `cos2theta=2cos^2theta-1`

`==>cos^2theta=(cos2theta+1)/2`

(b) `cos2theta=1-2sin^2theta`

`==>sin^2theta=(1-cos2theta)/2`

(c) `tan^2theta=(sin^2theta)/(cos^2theta)=(1-cos2theta)/(1+cos2theta)`

(d) `sin^thetacos^2theta=((1-cos2theta)/2)((1+cos2theta)/2)`

                    `=(1-cos^(2)2theta)/4`

                    `=(1-((1+cos2(2theta)))/2)/4`

                    `=(1+cos4theta)/8`

With some algebra you can find reduction formulas for higher powers. Please see reference for these formulas.

** I find it far more useful to be able to derive the formulas than to just memorize them. You really only need to memorize a few identities, and then know how to manipulate them. Of course, in a school setting it helps to know formulas, but in the long run you will find it far more helpful to understand how to get the formulas on your own.

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