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Question

prove the identity

2/1+cosx-Tan^2(x/2)=1

HOw did you do it?

Answer 1

I suggest that question is 2/(1+cosx) - tan^2(x/2)=1
We knew that sin^2(x/2)=½(1-cosx) and
cos^2(x/2)=½(1+cosx) then we get
Tan^2(x/2)=(1-cosx)/(1+cosx) So we entirely have
2/(1+cosx) - tan^2(x/2)=2/(1+cosx) - (1-cosx)/(1+cosx) =
(2-1+cosx)/(1+cosx)=(1+cosx)/(1+cosx)
=1

Answer 2

hello, the answer to your equation is that x could be any angle. this is because the two sides of the equation could be reduced to the same quantities,as follows:
2/1+cosx - tan^2(x/2)=1 substitute (1-cosx/1+cosx) for tan^2(x/2) - you can get this from the half angle identities in trigonometry;
therefore: 2/1+cosx -(1-cosx/1+cosx) = 1 - combining the like terms on the left side of the equation, you get:
2-1+cos x/1+cosx = 1; simplifying you get
1+cosx/1+cosx = 1, which works for any value that is substituted in x.
hence x can be any quantity or angle value in this case. I hope this helps.

Answer 3

use the formula tan^2 (x/2) = (1- cosx)/(1+cosx)

I am assuming your id is 2/(1+cosx) - tan^2(x/2) = 1
and not 2/(1-cosx-tan^2(x/2))

2/(1+ cosx) - (1-cosx)/(1+cosx)
= (2 - 1 + cosx)/(1+cosx)
= (1+cosx)/(1+cosx) = 1 = RHS

Answer 4

Please be more specific. Is it
2
------
1+cosx - tan^2(x/2)

= 1
or
2
---
1 + cosx

- tan^2(x/2)

= 1

Answer 5

No