Didn't we just do one like this? cos^2(x)- cos^4(x)= cos^2(x)- cos^2(x) cos^(x)= cos^2(x)(1- cos^2(x)). Does that help?tornzaer said:Homework Statement
cos^2x - cos^4x = cos^2x sin^2x
Homework Equations
N/A
The Attempt at a Solution
L.S. = cos^2x -(cos^2x)(cos^2x)
= cos^2x -cos^2x(cos^2x)
I'm stuck here. Am I doing something wrong during the first step? Thanks for your help.
Sort of but it's too cluttered.HallsofIvy said:Didn't we just do one like this? cos^2(x)- cos^4(x)= cos^2(x)- cos^2(x) cos^(x)= cos^2(x)(1- cos^2(x)). Does that help?
foil ...tornzaer said:= (cos^2x)(sin^2x)
= (cos^2x)(1-cos^2x)
God... how did I miss that. Thanks a lot.rocophysics said:foil ...
A trigonometric identity is an equation that is true for all values of the variables involved, typically involving trigonometric functions.
Trig identities are important because they allow us to simplify and manipulate trigonometric expressions, making them easier to work with and solve in mathematical problems.
Some common trig identities include the Pythagorean identities, double angle identities, and half angle identities.
To prove a trig identity, you need to use algebraic manipulation to transform one side of the equation into the other. This typically involves using known identities and properties of trigonometric functions.
The main difference between an identity and an equation is that an identity is always true, while an equation may only be true for certain values of the variables. In other words, an identity is an equation that is always true, regardless of the values of the variables involved.