SOLUTION: prove that {{{(cos^3X+Sin^3X)/(cosX+sinX)=(1-sinXcosX)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: prove that {{{(cos^3X+Sin^3X)/(cosX+sinX)=(1-sinXcosX)}}}      Log On


   

Question 1043835: prove that %28cos%5E3X%2BSin%5E3X%29%2F%28cosX%2BsinX%29=%281-sinXcosX%29
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28cos%5E3%28x%29%2Bsin%5E3%28x%29%29%2F%28cos%28x%29%2Bsin%28x%29%29=1-sin%28x%29cos%28x%29

recall: a%5E3%2Bb%5E3=%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29





cos%5E2%28x%29-cos%28x%29sin%28x%29%2Bsin%5E2%28x%29=1-sin%28x%29cos%28x%29.....rearrange left side

sin%5E2%28x%29%2Bcos%5E2%28x%29-sin%28x%29cos%28x%29=1-sin%28x%29cos%28x%29......since sin%5E2%28x%29%2Bcos%5E2%28x%29=1, we have

1-sin%28x%29cos%28x%29=1-sin%28x%29cos%28x%29