anonymous 5 years ago How do you simplifiy the expression: (1+ cot theta)(1-cot theta) - csc^2 theta ?

1. anonymous

could give clear eqautin

2. mathteacher1729

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. :)

3. anonymous

what math teacher said. nice

4. anonymous

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

5. anonymous

i completely understand the first part! thanks!

6. anonymous

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

7. anonymous

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

8. anonymous

okay I will. thanks!

9. anonymous

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

10. anonymous

nevermind. 2cot^2 theta right?

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

hold on i forgot the original question

15. anonymous

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

16. anonymous

ahhh thank you so much!!!!!