How do you rationalize? sqrt(1+cosy)/(1-cosy)

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Answer 1 · 2018-04-04T23:10:42

#(siny)/(1-cosy)#

# sqrt((1+cosy)/(1-cosy))#

Know: #sqrt(a/b)= sqrta/sqrtb#

So:
# sqrt((1+cosy)/(1-cosy))= sqrt(1+cosy)/sqrt(1-cosy)#

Rationalize by:
#sqrt(1+cosy)/sqrt(1-cosy)*sqrt(1-cosy)/sqrt(1-cosy)=#

#sqrt((1-cosy)(1+cosy))/(1-cosy)=#

Multiply binomials:
#sqrt((1-cos^2y))/(1-cosy)=#

Apply identity: #1-cos^2y= sin^2y#
#sqrt(sin^2y)/(1-cosy)=#

#(siny)/(1-cosy)#