We help IT Professionals succeed at work.

Proving trigonometry identities

jkk11
jkk11 asked
on
Medium Priority
973 Views
Last Modified: 2009-12-16
Prove that   1  over 1-cosx   -      1 over 1+cosx  =   2cotxcscx
Comment
Watch Question

CERTIFIED EXPERT
Most Valuable Expert 2014
Top Expert 2015
Commented:
1 /( 1-cosx)   -  1/( 1+cosx)
= (1+cosx)/((1+cosx)*(1-cosx)) - (1-cosx)/((1-cosx)*(1+cosx))

Not the solution you were looking for? Getting a personalized solution is easy.

Ask the Experts
Harisha M GEngineer
CERTIFIED EXPERT
Commented:
Hi,

1 /( 1-cosx)   -  1/( 1+cosx)
= (1 + cos x - 1 + cos x) / (1 - cos² x)
= 2cos x/sin² x
= 2(cos x/(sin x*sin x)
= 2(cos x/sin x)/sin x
= 2 tan x csc x

---
Harish
Commented:
1 /( 1-cosx)   -  1/( 1+cosx)

=

(1+cosx) - (1-cosx) all divided by (1-cosx)(1+cosx)

The numerator is 2cosx, the denominator 1-cos²x = sin²x

as cosx/sinx is cotx and 1/sinx is cscx, we get 2cotxcscx.

Q.E.D

Quite Easily Done.

BTW: This question is NOT worth 500 points. It looks anyway like home work and ought to be reduce to 50 points.
Access more of Experts Exchange with a free account
Thanks for using Experts Exchange.

Create a free account to continue.

Limited access with a free account allows you to:

  • View three pieces of content (articles, solutions, posts, and videos)
  • Ask the experts questions (counted toward content limit)
  • Customize your dashboard and profile

*This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

OR

Please enter a first name

Please enter a last name

8+ characters (letters, numbers, and a symbol)

By clicking, you agree to the Terms of Use and Privacy Policy.