Help with this math Transformation

Thread starter kasse
Start date Mar 7, 2007
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Transformation

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SUMMARY

The equation (cos(x))^2 = (1 + cos(2x))/2 is derived from trigonometric identities. The transformation utilizes the double angle formula for cosine, where cos(2x) = cos^2(x) - sin^2(x). By substituting this identity into the equation and simplifying, one can confirm the equality. The discussion emphasizes the importance of understanding these fundamental identities in trigonometry.

PREREQUISITES

Understanding of trigonometric identities, specifically the double angle formulas.
Familiarity with complex numbers and Euler's formula, cos(x) = (Exp(ix) + Exp(-ix))/2.
Basic algebraic manipulation skills for simplifying equations.
Knowledge of sine and cosine functions and their properties.

NEXT STEPS

Research the derivation and applications of the double angle formulas in trigonometry.
Study the relationship between sine and cosine functions, including their graphical representations.
Explore the use of Euler's formula in complex analysis and its implications in trigonometry.
Practice simplifying trigonometric expressions using identities and algebraic techniques.

USEFUL FOR

Students of mathematics, educators teaching trigonometry, and anyone interested in deepening their understanding of trigonometric identities and transformations.

Mar 7, 2007

kasse

Can anyone explain why (cos(x))^2 = (1+cos(2x))/2 ?

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Mar 7, 2007

ziad1985

cos(x)=(Exp(ix)+Exp(-ix))/2 right? do u know this formula?
square before and after the '='
then simplify it..

Mar 7, 2007

HallsofIvy

Science Advisor

Homework Helper

If you don't want to use complex numbers, remember that cos2x= cos² x- sin² x so that the right hand side is (1+ cos² x- sin²x)/2. Do you see an "obvious" way to simplify 1+ cos² x- sin²x?