How do you simplifiy the expression: (1+ cot theta)(1-cot theta) - csc^2 theta ?

Question

anonymous · Answer

could give clear eqautin

mathteacher1729 · Answer

Perfect square binomial: $$(1-x)(1+x)=1-x^2$$

In this case "x" = $\cot(\theta)$. 

So that means $ (1+\cot (\theta))(1-\cot (\theta)) = 1 - \cot^2(\theta)$

The expression is now $1-\cot^2(\theta) - \csc^2(\theta)$. 

We can use some trig identities here to reduce $1-csc^2(\theta) = -cot^2(\theta)$

Now our final answer is almost in front of us. :)

anonymous · Answer

what math teacher said.  nice

anonymous · Answer

u reduce it further by simplifying csc and cot..?

anonymous · Answer

i completely understand the first part! thanks!

anonymous · Answer

I'm just saying..its not an equation. it needs to be simplified to an expression

anonymous · Answer

rewrite everything (after last step) in terms of sine and cosine and it will be easier

anonymous · Answer

okay I will. thanks!

anonymous · Answer

so the answer is (1 - cot^2 theta) - csc theta right?

anonymous · Answer

nevermind. 2cot^2 theta right?

anonymous · Answer

well i guess there are many ways to write this.  i got

anonymous · Answer

we start with $$-cot^2(\theta)-csc^2(\theta)$$

anonymous · Answer

wait can I guess. thank you btw! i really appreciate your help.

-2cot^2 theta

anonymous · Answer

hold on i forgot the original question

anonymous · Answer

yes!  that is what i got after confusing myself.  good work

anonymous · Answer

ahhh thank you so much!!!!!