prove cotxcscx=cotx+cscx/sinx+tanx

Answer 1

This is a little confusing because you didn't use parenthesis on the right side of the equation but I'll assume you mean:

cot(x)csc(x) = [cot(x) + csc(x)]/[sin(x) + tan(x)]

cot(x)csc(x) = [cos(x)/sin(x) + 1/sin(x)]/[sin(x)/1 + sin(x)/cos(x)]

cot(x)csc(x) = [(cos(x) + 1)/sin(x)]/[cos(x)sin(x)/(cos(x) + sin(x)/cos(x)]

cot(x)csc(x) = [(cos(x) + 1)/sin(x)]/[cos(x)sin(x) + sin(x))/cos(x)]

cot(x)csc(x) = [(cos(x) + 1)/sin(x)]/[sin(x)(cos(x) + 1)/cos(x)]

cot(x)csc(x) = [(cos(x) + 1)/sin(x)] * cos(x)/[sin(x)(cos(x) + 1)]

cot(x)csc(x) = 1/sin(x) * cos(x)/sin(x)

cot(x)csc(x) = csc(x) * cot(x)

cot(x)csc(x) = cot(x)csc(x)

Answer 2

They are not equal!!--It should be written:

prove cot(x)csc(x) = (cotx+cscx)/(sinx+tanx)