Math Problem Statement
Berechne alle Lösungen a
Solution
To solve the equation provided:
we can proceed by simplifying the expression and solving for .
Step-by-Step Solution:
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Introduce a Substitution: Let . This substitution uses the Pythagorean identity .
With this substitution, the equation becomes:
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Simplify the Equation: Expanding gives , so the equation becomes:
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Clear the Denominator by Multiplying by : Multiply both sides by to eliminate the fractions:
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Rearrange the Equation into a Standard Quadratic Form: Bring all terms to one side of the equation:
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Solve the Quadratic Equation: Use the quadratic formula: Simplify the expression: [
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Algebra
Quadratic Equations
Formulas
1 + tan^2(α) = sec^2(α)
Quadratic equation formula: ax^2 + bx + c = 0
Theorems
Pythagorean identity
Quadratic formula
Suitable Grade Level
Grades 10-12
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