Question

Check these trigonometric identities?

tan(17π / 12)
cot(15°)

I got the same answers on both...not sure if that's right? It said I had to solve and leave it in reduced radical form.

Answer 1

tan(17pi/12)=tan(12pi/12+5pi/12)=tan(pi+5pi/12)=tan5pi/12=tan(pi/2-pi/12)=cot(pi/12)=cot(15)
There you go tan(17pi/12)=cot(15)

Answer 2

cot15 = cos15/sin15 = cos(60-45)/sin(60-45) and now expand
so cot16 = [(1+ rt3)/2rt2 ]/(rt3 - 1)/2rt2
= (1+rt3)/(rt3 - 1)
Hence it is the same answer for the other function too

Answer 3

this is a 3rd quadrant question where the angle is the same as tan(5pi/12) since tan is positive in 1st and 3rd quadrant

\[5\pi/12 = \pi/6 + \pi/4\]

so you need the double angle expansion of

\[\tan (\pi/6 + \pi/4)\]

\[\tan (\pi/6 ) = \sqrt{3}\] and tan (pi/4) = 1

the 2nd question is

cos(45 - 30) use the double angle expansion and exact values of cos(45) and cos (30)