Proving Trigonometric Identities (page 3 of 3)

When you were back in algebra, you rationalized complex and radical denominators by multiplying by the conjugate; that is, by the same values, but with the opposite sign in the middle. If the denominator was a complex value, like 3 + 4i, you would rationalize by multiplying, top and bottom, by 3 – 4i. In this way, you'd create a difference of squares, and the "i" terms would drop out, leaving you with the rational denominator 9 – 12i + 12i – 16i2 = 9 – 16(–1) = 9 + 16 = 25.

Every once in a very great while, you'll need to do something similar in other contexts, such as the following:

Don't expect always, or even usually, to be able to "see" the solution when you start. Be willing to try different things. If one attempt isn't working, try a different approach. Identities usually work out, if you give yourself enough time.

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