(1+cosx / 1-cosx) - (1-cosx/1+cosx) = (4cscx)(cotx)

For clarification with proper use of parentheses the identity is this:

(1+cosx)/(1-cosx) - (1-cosx)/(1+cosx) = 4 cscx cotx

Showing this is simply a matter of combining the two fractions and simplifying. Show us your attempt and we'll help you along.

Quote:

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Originally Posted by ebaines

For clarification with proper use of parentheses the identity is this:

(1+cosx)/(1-cosx) - (1-cosx)/(1+cosx) = 4 cscx cotx

Showing this is simply a matter of combining the two fractions and simplifying. Show us your attempt and we'll help you along.

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Ok so combining these two fractions on the left the two cosines would cancel out right? Or should I convert 1-cos x into sin^2 x? And then I would change csc x to 1/sin x. Making it 4/sin x. Change cot x to 1/tan x then cross multiply to get 4tan x /sin x. Tell me if Im on the right track

Cosines do NOT cancel out, and 1-cosx doed not equal sin^2x.

To combine these fractions multiply the first one by (1+c)/(1+c) and the second one by (1-c)(1-c), and that way they end up with common denominators:



Now continue to simplify and see where it takes you.