verify 1sin xcsc x1 cot xcos xSolution1sin xcsc x1 cot xco

verify (1-sin x)(csc x+1) = cot x(cos x)

Solution

(1-sin x)(csc x+1) = cot x(cos x)

LHS (1-sin x)(csc x+1)

expanding: cscx +1 -sinxcscx -sinx

cscx +1 -1 -sinx

cscx - sinx

1/sinx -sinx

(1-sinx^2x)/sinx

cos^2x/sinx

(cosx/sinx)*cosx

cotx(cosx)

RHS