Tuesday, August 13, 2013

show that cos(2arcsinx)=1-2x2

using double angle formulas we write: 
cos%282theta%29=1-2sin%5E2%28theta%29%0D%0A%0D%0A 
with 
theta=arcsin%28x%29 

then we notice: 
sin%28theta%29=sin%28arcsin%28x%29%29=x 

and therefore 
cos%282arcsinx%29=cos%282theta%29=1-2sin%5E2%28theta%29=1-2x%5E2%0D%0A%0D%0A 


:)
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