Question #1ff8a

1 Answer
Noah G
Feb 14, 2018

This equals #2#

Explanation:

We have:

#=(cot^2theta + 2cottheta + 1 - csc^2theta)/cottheta#

#=cot^2theta/cottheta + 2cottheta/cottheta + 1/cottheta - csc^2theta/cottheta#

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

#=cottheta + 2 +1/cottheta - 1/(sinthetacostheta)#

#=costheta/sintheta + 2 + sintheta/costheta - 1/(sinthetacostheta)#

#=(cos^2theta + sin^2theta)/(costhetasintheta) - 1/(sinthetacostheta) + 2#

We know that #sin^2theta + cos^2theta = 1#.

#=1/(costhetasintheta) - 1/(sinthetacostheta) + 2#

#=0 + 2#

#=2#

Hopefully this helps!

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