## starwars18 one year ago Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

1. starwars18

$\frac{ \sin x }{ 1 - \cos x } + \frac{ \sin x }{ 1 + \cos x } = 2 \csc x$

2. dan815

okay first thing to know is csc(x) = 1/sin(x)

3. starwars18

yes

4. dan815

you should simplify the left side, by multiplying both fracctions by the conjugate

5. dan815

1-cos(x) and 1+cos(x) are factors of 1-(cos(x))^2

6. dan815

and 1-cos^2(x) = sin^2(x) as sin^2(x) + cos^2(x) = 1 this identity comes from the unit circle

7. dan815

okay yep it is right 2/sin(x) = 2csc(x) should be the right answer

8. starwars18

so sin x * (1 + cos x) + sin^3 x

9. starwars18

so they all cancel out leaving 2 over sin x... i get it now

10. anonymous

2 / sin(x) is like saying 2 times 1 /sin(x) which mean 2 times csc(x) or 2 csc(x) since csc = 1/sin(x)

11. starwars18

yes, ty i got it. sorry i forgot to close the question!!!