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#