Solving tan(x) + cot(x) = 2

Trigonometry · Axiom Academy

EXAMPLE Solving tan(x) + cot(x) = 2 Learn to convert trigonometric functions to sines and cosines, then solve the resulting equation. Excellent work! You've successfully solved a complex trigonometric equation. Here's what we learned: Converting to Fundamental Functions: When faced with tangent and cotangent, convert them to sine and cosine for easier manipulation. Common Denominator Strategy: Finding a common denominator allows us to combine fractions and simplify complex expressions. Pythagorean Identity: sin²(x) + cos²(x) = 1 is one of the most powerful tools in trigonometry. Watch for opportunities to use it! Double-Angle Formulas: Recognizing that sin(x)cos(x) = sin(2x)/2 helps transform products into single functions. General Solutions: Trigonometric equations have infinitely many solutions. Always express your answer with "+ nπ" or "+ 2πn" as appropriate. This systematic approach—converting to sines/cosines, finding common denominators, and using identities—is your roadmap for solving many challenging trigonometric equations!

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