Question 1042158
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Hi i have to solve this problem, thanks for help.

Sin^4x - Cos^4x = Sin^2x - Cos^2x
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Are you familiar with this identity: {{{a^2 - b^2}}} = {a+b)*(a-b)?


If not, or if you are not sure, look into the lesson <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-difference-of-squares-formula.lesson>The difference of squares formula</A> in this site.



OK. Now, apply this identity to the left side. You will get


{{{Sin^4(x) - Cos^4(x)}}} = {{{(sin^2(x) + cos^2(x))*(sin^2(x) - cos^2(x))}}}.

But the first parentheses,  {{{(sin^2(x) + cos^2(x))}}} is equal to 1, as everybody knows.

Therefore, 

{{{Sin^4(x) - Cos^4(x)}}} = {{{sin^2(x) - cos^2(x)}}}.

QED.
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