Find tan5x in terms of tanx.

Not sure if I'm meant to manipulate z=cosx+isinx to get z/cosx=1+itanx?

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- Mar 2nd 2009, 07:27 AMErghhhDe Moivre's theorem.
Find tan5x in terms of tanx.

Not sure if I'm meant to manipulate z=cosx+isinx to get z/cosx=1+itanx? - Mar 2nd 2009, 06:17 PMSoroban
Hello, Erghhh!

It can be done, but I don't know if my method is what they want.

Quote:

Use DeMoivre's Theorem to find in terms of

So we have: .

. .

. .

Equate real and imaginary components:

. .

. .

We have: .

Divide top and bottom by

. . Therefore: .

- Mar 2nd 2009, 07:23 PMSoroban

We**never**have to go through all that ever again!

These multiple-angle formulas can be written with a rhythmic pattern.

Suppose we want: .

Expand: .

. .

Write these terms alternately in the denominator and numerator of a fraction.

Start with the denominator: .

Insert alternating signs in the numerator and in the denominator:

. . . . . . .

And we have two of the multiple-angle identities:

Numerator: . .

Denominator: .

For divide top and bottom of the fraction by

. .