What are trig identities?can you please help me with this problem?

Questions
1

Hello,

  1. I’m confused on what are exactly all the trig identities. My professor is very unclear. What are the trig identities used for? Is is just something I need memorize?

  2. Can someone help me prove this:

sin(x)/(1+cos(x)) + (1+cos(x))/sin(x) = 2csc(x)

Any help would be appreciated.
Thank you.

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3

Here’s a simplified step-by-step solution:

sin(x)/(1+cos(x)) + (1+cos(x))/sin(x) = 2csc(x)

Multiply by sin(x)

sin(x)^2/(1+cos(x)) + (1+cos(x))= 2

Use sin(x)^2=1-cos(x)^2={1+cos(x)) (1-cos(x))

Thus 1-cos(x) +1+cos(x) = 2

QED

4

Thank you so much. I understand it now.
I needed to know it for my midterm today.