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Precalculus: proving trigonometric identity

  • #1

Homework Statement



prove that: tan(1+cos(x))^2 = 1-cos(x)

Homework Equations



trig identities, like the pythagorean, sum/difference, double/half angle identities, power reducing identities, etc...

The Attempt at a Solution



i'm not sure where to start; i tried using the pythagorean identity where 1+tan(X)^2 = sec(x)^2, but couldn't get anywhere after that :\

then i used my calculator and made X a random number. i typed in the left side expression, and pressed enter. i then typed in the right hand expression, and pressed enter. the two values were different. what did i do wrong?
i'm not really sure anymore that its even possible to prove the above...
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
You're right. It's not an identity. Just put x=0. Then you don't even need a calculator. Must be some mistake here.
 
  • #3
214
1
If I'm write you want to write [tex]tan(1 + cos x)^2[/tex] = 1 - cos(x). I think it is not possible to prove because if cos (x) is zero then [tex]{tan}^2{1}[/tex] is not equal to 1. Even if the equation is [tex]tan(1 + {cos}^2{x})[/tex] then also you can't prove it. I think, the problem is not to prove but to solve.
 

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