Question 439286
{{{(tan(x) -cot( x))/(tan x+cot x)}}}=2(sin^2)x




use identities:

{{{sin(x) / cos(x) }}}

{{{cot(x) = cos(x)/ sin(x)}}}

prove that left side is equal to right side:

{{{(tanx -cotx)/(tanx+cot x)}}} =2sin^2x -1


{{{(sinx/cosx -cosx/sinx)/(sinx/cosx+cosx/sinx)}}} = 2sin^2 x - 1




{{{(sin^2(x)- cos^2(x))/sin(x)cos(x))/((sin^2(x)-cos^2(x))/(sin(x)cos(x)))}}}= 2sin^2 x - 1



{{{((sin^2(x)- cos^2(x))/cross(sin(x)cos(x)))/((sin^2(x)+cos^2(x))/cross((sin(x)cos(x))))}}}= 2sin^2 x - 1


{{{(sin^2(x)-cos^2(x))/(sin^2(x)+cos^2(x))}}}= 2sin^2 x - 1...notice that both nominator and denominator have sin and coc squared


{{{(sin^2(x)-cos^2(x))/1}}}= 2sin^2 x - 1


replace cos^2x with {{{1-sin^2(x)}}}


{{{sin^2(x)-(1-sin^2(x))}}}= 2sin^2 x - 1


{{{sin^2(x)-1+sin^2(x)}}}= 2sin^2 x - 1

{{{2sin^2(x)-1}}}= 2sin^2 x - 1