Verify that the equation is an identity. Show that ((tanx)(sinx))/((tanx)-(sinx)) = ((sinx)/(1-cosx)). Please show all steps and the rules that apply to them.

Answer 1

tanxsinx/(tanx-sinx) = (sinx/cosx)sinx/(sinx/cosx -sinx)

= sin²x/(cosx(sinx/cosx - sinx) distribute cosx in denominator

= sin²x/(sinx-sinxcosx) factor denominator

= sin²x/(sinx(1-cosx)) Cancel sinx out of numerator and denominator

= sinx/(1-cosx)