Trig Substitution Problem w/ tan substitution

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SUMMARY

The discussion centers on a trigonometric substitution problem involving the tangent function. A participant identifies an error in their solution related to the cosecant formula, specifically missing a square root in their calculations. The conversation highlights the importance of correctly applying Pythagoras' Theorem in trigonometric contexts. Ultimately, the participants clarify the dimensions of triangle sides and the hypotenuse, emphasizing the need for accuracy in mathematical expressions.

PREREQUISITES
  • Understanding of trigonometric identities
  • Familiarity with Pythagoras' Theorem
  • Knowledge of trigonometric substitution techniques
  • Basic geometry of right triangles
NEXT STEPS
  • Review trigonometric identities and their applications
  • Practice problems involving trigonometric substitution with different functions
  • Study the derivation and application of Pythagorean identities
  • Explore advanced techniques in calculus involving trigonometric integrals
USEFUL FOR

Students studying calculus, particularly those tackling integration techniques involving trigonometric functions, as well as educators looking for examples of common errors in trigonometric substitution.

Burjam
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Homework Statement



Under #3

Homework Equations



Trig identities

The Attempt at a Solution



The picture attached is my attempt. The square in the upper upper left is the problem and the one in the lower right is my solution. I'm seeing that I'm getting the wrong answer, but not how.

1479619739190-1775315430.jpg
 
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You should type in the problem at least.
The formula for csc (theta) is wrong, You miss a square root.
 
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I miss a square root? Where does a square root come into play? None of the sides of the triangle should have a square root in them.
 
Burjam said:
I miss a square root? Where does a square root come into play? None of the sides of the triangle should have a square root in them.
Really? So the dimension of the sides of a right triangle is length, but that of the hypotenuse is length-squared?
Recall Pythagoras' Theorem.
 
Haha sorry I did this while really tired... my bad.
 

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