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David Cohen questions just for fun.
Enjoy.
Enjoy.
is not true statement![]()
tan(x/2)=(1-cos(x)+sin(x))/(1+cos(x)+sin(x))
manipulate right side
(1-cos(x)+sin(x))/(1+cos(x)+sin(x))............ 1-cos(x)=2sin^2(x/2), 1+cos(x)=2cos^2(x/2)
=(2sin^2(x/2)+sin(x))/(2cos^2(x/2)+sin(x))
=(2 sqrt(2) sin(x/2 + π/4) sin(x/2))/(2sqrt(2) sin(x/2 + π/4) cos(x/2))
= sin(x/2)/cos(x/2)
= tan(x/2)
Prove the identity
cot(x) / csc(x) = cos(x)