Find tan5x in terms of tanx.
Not sure if I'm meant to manipulate z=cosx+isinx to get z/cosx=1+itanx?
Hello, Erghhh!
It can be done, but I don't know if my method is what they want.
DeMoivre's Theorem says: .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: .
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
. .