Proving a Trigonometric Identity

Question

sinx/1+cosx+1+cosx/sinx=2cscx

I need to get the left side to look like the right side using trig identities, if anyone can help with steps, that would be awesome! Thanks!

Answer 1

sin 1 + cos

--------- + ------------

1 + cos sin

common denominator is sin ( 1 + cos)

When combined into a single fraction:

sin^2 + (1+cos)^2

---------------------

sin (1 + cos)

FOILs the numerator:

sin^2 + 1 + 2 cos + cos^2

--------------------------

sin (1 + cos)

Trig identity: sin^2+cos^2 = 1

1 +1 + 2 cos

-------------

sin (1 + cos)

combines:

2 + 2 cos

-------------

sin (1 + cos)

factors out 2 in the numerator

2 ( 1+ cos)

------------

sin (1 + cos)

1+ cos cancels out:

2

------------

sin

2 csc