How do you simplify the expression $(sint(1+sint))/(1-cos^2t)-1$ ?

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Answer 1 · 2016-08-25T01:46:23

Simplified, your expression equals $csct$ .

Start by distributing:

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

Use the identity $sin^2x + cos^2x = 1 -> sin^2x = 1- cos^2x$ to rearrange the denominator.

$=(sint + sin^2t)/sin^2t - 1$

Put on a common denominator.

$=(sint + sin^2t - sin^2t)/sin^2t$

$=(sint)/sin^2t$

$=1/sint$

Finally, apply the identity $1/sintheta = csctheta$ .

$=csct$

How do you simplify the expression (sint(1+sint))/(1-cos^2t)-1(sint(1+sint))/(1-cos^2t)-1?