Question 822716
Prove the identity:
A) Sinx( sec x-csc x) = tanx-1
start with left side:
{{{sin(x)(1/cos(x))-(1/sin(x))=sin(x)/cos(x)-sin(x)/sin(x)=tan(x)-1}}}
verified:left side=right side
..
B) (cot x-1)^2 = 1-sin2x/ sin^2 x
stare with left side:
{{{(cot(x)-1)^2=cot^2(x)-2cot(x)+1=cos^2(x)/sin^2(x)-2cos(x)/sin(x)+1=(cos^2(x)-2cos(x)sin(x)+sin^2(x))/(sin^2(x))=(1-sin(2x))/sin^2(x)}}}
verified:left side=right side