Question 441226
We transform the right side until reach the same expression as the left side:

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

= {{{(cotx)^2(sinx-cosx)/(2(sinx)^2-(sinx)^2-(cosx)^2)}}}=

= {{{(cotx)^2(sinx-cosx)/(sinx+cosx)(sinx-cosx)=(cotx)^2/(sinx+cosx)}}}, thus 

the identity is true.