Question

Help me prove LHS is equal to RHS?
(sin x/1-cos x) + (sin x/1+cos x) = 2 csc x

Answer 1

@Mertsj

Answer 2

@plohrr

Answer 3

@jim_thompson5910

Answer 4

Write the two fractions on the left as a single fraction using the common denominator (1-cosx)(1+cosx)

Answer 5

Distribute.

Answer 6

So we get sin/1-cos^2?

Answer 7

Here is what you get:
\[\frac{\sin x(1+\cos x)+\sin x(1-\cos x)}{(1-\cos ^2x)}\]

Answer 8

How did you get that?

Answer 9

Th original was:
\[\frac{ \sin x }{ 1-\cos x } + \frac{ \sin x }{ 1 + \cos x} = 2 \csc x\]

Answer 10

Write these two fractions with a common denominator:
\[\frac{3}{7}+\frac{3}{11}=\frac{3(11)+3(7)}{7(11)}\]

Answer 11

Now apply that principal to your problem

Answer 12

Oh, okay. I see now. Hang on just a minute. :P

Answer 13

Does the cos x sin x and -cos x sin x cancel out?

Answer 14

You now have a 2 term numerator. The two terms have sin x as a common factor. Factor it out.

Answer 15

I don't get it..