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Verifying Trig Identity

  • Thread starter Trizz
  • Start date
  • #1
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Homework Statement



sec^2(x) tan^2(x) + sec^2(x) = sec^4(x)

Homework Equations



sin^2 + cos^2 = 1
1+tan^2 = sec^2
1+cot^2 = csc^2

The Attempt at a Solution



First, I changed everything to sin and cos to try and make it clearer.

1/cos^2 * sin^2/cos^2 + 1/cos^2 = sec^4
sin^2/cos^4 + 1/cos^2

Then I multiplied by the common denominator, cos^2

sin^2 * cos^2/cos^6 + cos^2/cos^4

Where do I go from here??
 

Answers and Replies

  • #2
867
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You don't need to multiply the first term by cos2x/cos2, just the second so they have a common denominator. Then add the fractions and use an identity.
 
  • #3
Mentallic
Homework Helper
3,798
94
You don't need to change everything into sinx and cosx to makes things clearer. Even if you can't think about what secx is without thinking of 1/cosx you can still solve this problem:

Set the equation to 0, then factorize by a common factor which should obviously be [itex]sec^2x[/itex]. Now use an identity.
At this point, if you're confused about what has happened just think about this: for the equation x-x=0, you can have any value of x to satisfy the equation. This means all x values are the equation's solutions.

But also remember that [itex]0/0\neq 0[/itex] so make sure to show that the solutions to [itex]cosx= 0[/itex] are excluded from the solutions in the original equation (This is from the first factor [itex]sec^2x[/itex]).
 

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