Question 749613
Please help me prove the following identities: 
a) cot^2σsin^2σ + sin^2σ=1
{{{cot^2(x)sin^2(x)+sin^2(x)=sin^2(x)(1+cot^2(x))=sin^2(x)(1+(cos^2(x)/sin^2(x)))=sin^2(x)+cos^2(x)=1}}}
..
b) cosσsecσ/1+tan^2σ=cos^2σ
{{{(cos(x)sec(x))/(1+tan^2(x))=(cos(x)sec(x))/(sec^2(x))=(cos(x))/(sec(x))=cos^2(x)}}}
..
c) sin2x/1+cos2x=tanx
{{{sin(2x)/(1+cos(2x))=(2sin(x)cos(x))/(1+(1-2sin(x)))=(2sin(x)cos(x))/(2(1-sin^2(x)))
=(2sin(x)cos(x))/(2(cos^2(x)))=sin(x)/cos(x)=tan(x)}}}
d) csc2A = cot2A= cotA
??