SOLUTION: Show the following identities. A). {{{cosx+sinx/cosx-sinx - cosx-sinx/cosx+sinx = 2tan2x}}} B). {{{cos^4theta - sin^4theta = cos 2theta}}} C). {{{ (cos(alpha+bet

Algebra ->  Trigonometry-basics -> SOLUTION: Show the following identities. A). {{{cosx+sinx/cosx-sinx - cosx-sinx/cosx+sinx = 2tan2x}}} B). {{{cos^4theta - sin^4theta = cos 2theta}}} C). {{{ (cos(alpha+bet      Log On


   

Question 1129886: Show the following identities.
A). cosx%2Bsinx%2Fcosx-sinx+-+cosx-sinx%2Fcosx%2Bsinx+=+2tan2x
B). cos%5E4theta+-+sin%5E4theta+=+cos+2theta
C).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A).
















%282cos%28x%29sin%28x%29%2B2cos%28x%29sin%28x%29%29%2F%282cos%5E2%28x%29-1%29=+2tan%282x%29..............use sin%282x%29+=+2sin%28x%29cos%28x%29 and 2cos%5E2%28x%29-1=cos%282+x%29

%28sin%282x%29%2Bsin%282x%29%29%2Fcos%282+x%29+=+2tan%282x%29

%282sin%282x%29%29%2Fcos%282+x%29+=+2tan%282x%29

2tan%282x%29+=+2tan%282x%29



B).
cos%5E4%28theta%29+-+sin%5E4%28theta%29+=+cos%282theta%29

%28cos%5E2%28theta%29%29%5E2+-+%28sin%5E2%28theta%29%29%5E2+=+cos%282theta%29







%28%282cos%5E2%28theta%29+-+1%29%281%29%29+=+cos%282theta%29
2cos%5E2%28theta%29+-+1+=+cos%282theta%29
cos%282theta%29++=+cos%282theta%29


C).














+ctg%28alpha%29+%2Atan%28alpha%29+=+1


+1+=+1