Expert: Abe Mantell - 1/11/2005

Question
i dont know where to start with this problem;
 Prove that the equation is an identity
sinX/(1-cosX) + (1-cosX)/sinX = 2 cscX

please send as soon as possible
THANK YOU

Answer
Hello Kate,

OK, combine the left side by getting a common denominator,
which is sin(x)[1-cos(x)]:
==>[sin(x)^2 + (1-cos(x))^2]/[sin(x)(1-cos(x))]
= [sin(x)^2 + 1 - 2cos(x) + cos(x)^2]/[sin(x)(1-cos(x))]
= [sin(x)^2 + cos(x)^2 + 1 - 2cos(x)]/[sin(x)(1-cos(x))]
= [1 + 1 - 2cos(x)]/[sin(x)(1-cos(x))]
= [2 - 2cos(x)]/[sin(x)(1-cos(x))]
= 2[1-cos(x)]/[sin(x)(1-cos(x))]
= 2/sin(x)
= 2csc(x)

OK?

Abe