Find the exact value of tan 285 deg + cos 75 deg + cot 60 deg

[markm]

the question is: find the exact value of tan 285 deg + cos 75 deg + cot 60 deg

i tried converting them to radians and got

tan 5pi / 12 + cos 5 pi / 12 + cot pi / 3

by "exact value", the question means fractions, not decimals. as far as i know, only the cot part has some special identity. am i missing something important? we have a long test tomorrow..

thanks in advance for any help. ^_^

 

[dextercioby]

Use the fact that
$$\tan x=\frac{1}{\cot x}=\frac{\sin x}{\cos x}$$

Daniel.

 

[markm]

that still wouldn't help because 5pi/12 has no special values (i.e. sin pi/6 = 1/2, sin pi/3 = sqrt3 / 2, etc.). it's not a special angle in the unit circle.. :(

 

[dextercioby]

$$\sin\frac{5\pi}{12}=\sin(\pi-\frac{\pi}{3}-\frac{\pi}{4})=\sin(\frac{2\pi}{3}-\frac{\pi}{4})$$

which involves "special angles"...

Daniel.

 

[markm]

thanks a lot. :)