Simplifying Trig Expressions help #2. Can someone please help me?

cot^2θ/1+cscθ+sinθcscθ #cot^2θ/(1+cscθ)+sinθcscθ#
Sorry for posting these questions. This one seems to be the trickiest.

1 Answer
Noah G
Mar 30, 2018

So I'm assuming the question is

#cot^2theta/(1 +csctheta) + sinthetacsctheta(cot^2theta)/(1 +csctheta) + sinthetacsctheta#

As you can see, #csctheta = 1/sintheta#, so #1/sintheta(sin theta) = 1#.

#(2cot^2theta)/(1 + csctheta) + 1#

#(2cos^2theta/sin^2theta)/(1 + 1/sintheta) + 1#

#((2cos^2theta)/sin^2theta)/((sin theta + 1)/sintheta) + 1#

#(2cos^2theta)/(sintheta(sin theta+ 1)) + 1#

#(2(1 - sin^2theta))/(sintheta(sin theta + 1))+ 1#

#(2(1 - sin theta))/sintheta + 1#

#(2 - 2sintheta + sin theta)/sintheta#

#(2 - sin theta)/sintheta#

#2csctheta - 1#

Hopefully this helps!

Related questions
Impact of this question
930 views around the world
You can reuse this answer
Creative Commons License