Question

(cscx-cotx)/tanx = cosx/(1+cosx) How do I get from the left side to the right side with trig identities?

Answer 1

Oops, misread...

Answer 2

Multiply top and bottom by sin(x)
\[ \frac{1 - \cos(x)}{\sin^2(x) / \cos(x)} \]
Bring the bottom cosine up top:
\[ \frac{\cos(x) - \cos^2(x)}{\sin^2(x)} \]
factor out a cosine from the numerator, and rewrite the denominator:
\[\frac{\cos(x) \left( 1 - \cos(x)\right)}{1 - \cos^2(x) } = \frac{\cos(x)\left(1-\cos(x)\right)}{(1+\cos(x) )(1 - \cos(x))} \]
Cancel appropriately to get
\[ \frac{\cos(x)}{1+\cos(x)} \]