sinxcscxcotx simplifySolutionsinx cosec x cot x cosec x 1si

sinx/(cscx+cotx) simplify.

sinx /(cosec x + cot x)

cosec x= 1/sin x and cot x=cosx/sinx

therefore,

=sinx/((1/sinx)-(cosx/sinx))

=sin x/((1-cos x)/sinx)

=sin²x/(1+cos x)

and sin²x=1-cos²x

=(1-cos²x)/(1+cos x)

factoring 1-cos²x=(1-cos x)(1+cos x)

=(1+cos x)(1-cosx)/(1+cos x)

=1-cosx

Therefore sin²x/(cosecx - cotx)= 1- cos x