Trigonometry Workbook For Dummies
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When the trig expression you're given begins with fractions, most of the time you have to add (or subtract) them to get things to simplify. Here's one example of a proof where doing just that gets the ball rolling. Say you have to find the lowest common denominator (LCD) to add the two fractions in order to simplify this expression:

A trigonometric function with fractions.

With that as the beginning step, follow along:

  1. In order to add these fractions, you must find the LCD of the two fractions.

    The least common denominator is

    The lowest common denominator in a function.

    so multiply the first term by

    Cosine over cosine.

    and multiply the second term by

    1 plus sine divided by one plus sine.

    You get

    Two trigonometric expression with a common denominator.
  2. Multiply or distribute in the numerators of the fractions.

    Multiplying or distributing the numerators of a fraction.
  3. Add the two fractions.

    Adding two fractions with a common denominator
  4. Look for any trig identities and substitute.

    You can rewrite the numerator as

    A Trigonometric expression with a fraction.

    which is equal to

    Replacing any trig identities in an expression.

    because cos2 t + sin2 t = 1 (a Pythagorean identity).

  5. Cancel or reduce the fraction.

    After the top and the bottom are completely factored, you can cancel terms:

    Factoring the components of a fraction.
  6. Change any reciprocal trig functions.

    Final result of trigonometric expression.

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