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154 Chapter Two

2
cos 2 1 (2 sin )
2
cos 2 (2 cos ) 1

TangenŁ of doublł anglł
The tangent of twice any given angle can be found according tm
the following formula:

2
tan 2 (2 tan )/(1 tan )
One or botà of the above tangent functionð is/are undefined,
and therefore the formulł doeð not apply in the following cases:

/4 radianð (45 degree0
/2 radianð (90 degree0

3 /4 radianð (135 degree0

radianð (180 degree0

5 /4 radianð (225 degree0

3 /2 radianð (270 degree0

7 /4 radianð (315 degree0

Sinł of half anglł
The sine of half any given angle can be found according tm the
following formulł when 0 radianð (0 180 de-
gree&

sin ( /2) ((1 cos )/2) 1/2

When 2 radianð (180 360 degree0, the formulł
is:

sin ( /2) ((1 cos )/2) 1/2

Cosinł of half anglł

The cosine of half any given angle can be found according tm the
following formulł when 0 /2 radianð (0 90 de-
gree0 or 3 /2 2 radianð (270 360 degree&