Common Trigonometry Mistakes
Example: Simplifying a trigonometric expression

Some problems provide the opportunity for more than one mistake.

The Goal

Simplify the expression:


The Mistakes

Find the mistakes:



(Roll the mouse over the math to see hints in red)



(Roll the mouse over the math to see hints in red and green)

The Correction


(Roll the mouse over the area above to see the correction in blue)


The first attempted solution has two mistakes; in the second step the second fraction's numerator should have had all terms multiplied by sin(x). In the third step the minus sign was not distributed correctly.

Two incorrect cancellations mar the second attempted solution. A multiplicatively cancelled part must be a common factor of numerator and denominator (first mistake). An additively cancelled part must be exactly the same term (second mistake). Note sin(x) is a factor of all terms in the numerator, and should have been cancelled from all terms (first error). For the second error, 2cos2(x)sin(x) is not equal to 2cos2(x). There's also a sign change mistake shown in green.

The keys to solving this problem are knowing the correct double angle formulas (correct in both of these attempted solutions) and then using careful algebra to complete the simplification.

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