Question

find the exact value of tan(19pi/12) using sum and difference identities. No decimal answers!

Answer 1

\[\frac{19\pi}{12}=\frac{10\pi}{12}+\frac{9\pi}{12}=\frac{5 \pi}{6}+\frac{3\pi}{4}\]

Answer 2

JDC: Having forgotten the sum formula for the tangent function, I did an Internet search and came up with the following (which may be of interest and help to you):

http://home.windstream.net/okrebs/page102.html Please refer to this and copy down the formula for tan (alpha + beta).

Mertsj has kindly done some of the groundwork for us, showing that 19pi/12 = 5pi/6 + 3pi/4.

Thus, tan 19pi/12 = tan (5pi/6 + 3pi/4). Let alpha=5p/6 and beta=3pi/4. Then tan alpha=-1/Sqrt(3), and tan beta=-1.

Just substitute these values into the formula for tan (alpha + beta).