Question

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

Answer 1

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

Answer 2

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

Answer 3

yes

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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)

Answer 11

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