How do you simplify the expression #sint/(1-cost)+(1-cost)/sint#?

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Answer 1 · 2017-01-01T04:44:26

Put on a common denominator.

#=((Sint)(Sint))/(sint(1-cost)) + ((1-cost)(1-cost))/(sint(1-cost))#

#=(sin^2t + 1 - 2cost + cos^2t)/(sint(1-cost))#

Use the identity #sin^2theta + cos^2theta = 1#.

#=(1 + 1 - 2cost)/(sint(1-cost))#

#=(2 - 2cost)/(sint(1-cost)#

Factor:

#= (2(1 - cost))/(sint(1-cost))#

#=2/sint#

Use #csctheta = 1/sintheta#.

#=2csct#

Hopefully this helps!