Question #781b9

1 Answer
Nov 29, 2016

We will use the following:

  • #cot(x) = cos(x)/sin(x)#
  • #csc(x) = 1/sin(x)#
  • #sin^2(x)+cos^2(x) = 1#
    #=> cos^2(x) = 1-sin^2(x)#
  • #a^2-b^2 = (a+b)(a-b)#

#cot^2(x)/(1+csc(x)) = (cos(x)/sin(x))^2/(1+1/sin(x))#

#=(cos^2(x)/sin^2(x))/(1+1/sin(x))#

#=cos^2(x)/(sin^2(x)+sin(x))#

#=(1-sin^2(x))/(sin(x)(1+sin(x)))#

#=((1+sin(x))(1-sin(x)))/(sin(x)(1+sin(x)))#

#=(1-sin(x))/sin(x)#