How do you simplify #1+cot^2theta-cos^2theta-cos^2thetacot^2theta#?

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Answer 1 · 2017-02-04T15:35:55

#1#

#=1 + cot^2theta - cos^2theta(1 + cot^2theta)#

We can now simplify using #1 + cot^2alpha = csc^2alpha#.

#= csc^2theta - cos^2theta(csc^2theta)#

#=csc^2theta - cos^2theta(1/sin^2theta)#

Use #cosalpha/sinalpha = cotalpha#:

#=csc^2theta - cot^2theta#

Rearrange the above identity to get #1 = csc^2alpha - cot^2alpha#

#=1#

Hopefully this helps!