Question

Simplify ((cosθ)/(1+sinθ) - (cosθ)/(sinθ -1))^-1

a) cosθ/2
b) 2secθ
c) 2sinθ
d) cscθ/2

Answer 1

\[\frac{\cos{θ}}{1+\sin{θ}}-(\frac{\cos{θ}}{\sin{θ}-1})^{-1}?\]

Answer 2

\[(\frac{a}{b})^{-1}=\frac{b}{a}\]

Answer 3

the ^-1 is for the whole equation

Answer 4

oh so I flip both parts?

Answer 5

oh well then you'll have to solve by greatest common multiple I think. make it one fraction

Answer 6

(1+sinθ)(sinθ-1) denominator,

Answer 7

sorry I've got homework of my own so I'm not sure if I can stay here

Answer 8

oh it's okay thank you for your help (:

Answer 9

np. do you get what I'm saying though? make a common denominator ?

Answer 10

yes i do

Answer 11

alright, do you think you can do it from here? I might be able to help but I'm not certain

Answer 12

you just multiply the denominator to both sides right?

Answer 13

well the left side multiplies by (1+sinθ/1+sinθ) and the right fraction multiplies by (sinθ-1/sinθ-1)

Answer 14

yeah

Answer 15

then you find any identities in the resulting fraction, and simplify

Answer 16

that's how I learned to do it ☺

Answer 17

im actually not sure what the answer should be. I got "a" as the answer

Answer 18

oh. I'm sorry I don't have enough time to help you u_u
@Directrix ?

Answer 19

\[\frac{1}{\frac{\cos (\theta )}{\sin (\theta )+1}-\frac{\cos (\theta )}{\sin (\theta )-1}}=-\frac{1}{\frac{2 \cos (\theta )}{(\sin (\theta )-1) (\sin (\theta )+1)}}=-\frac{1}{\frac{2 \cos (\theta )}{\sin ^2(\theta )-1}}=-\frac{1}{-\frac{2 \cos (\theta )}{\cos ^2(\theta )}}=\frac{\cos (\theta )}{2} \]