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!

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