Question

verify (1/(sinx+1)) + (1/(cscx+1))=1

Answer 1

(1 / sin(x) + 1) + (1/csc(x) + 1)

put fractions over a common denominator:

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

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

= [csc(x) + sin(x) + 2] / [sin(x)csc(x) + sin(x) + csc(x) + 1]

as csc(x) = 1/sin(x), we have:

= [csc(x) + sin(x) + 2] / [sin(x)(1/sin(x)) + sin(x) + csc(x) + 1]

= [csc(x) + sin(x) + 2] / [1 + sin(x) + csc(x) + 1]

= [csc(x) + sin(x) + 2] / [sin(x) + csc(x) + 2]

= 1
as required.

Answer 2

thanks thats what i got