1/3cos30°/1/2sin45°+tan60°/cos30°?

1 Answer
May 5, 2018

# {6+\sqrt{6}}/3 #

Explanation:

Oh my gosh, can't they come up with a trig problem that's not 30/60/90 or 45/45/90?

# {1/3 cos 30^circ }/{1/2 sin 45^circ} + tan60^circ/cos 30^circ #

# = {2 cos 30^circ }/{3 sin 45^circ } + cot 30^circ / cos 30^circ #

# = {2 cos 30^circ }/{3 sin 45^circ } + {cos 30^circ / sin 30^circ } / cos 30^circ #

# = {2 cos 30^circ }/{3 sin 45^circ } + 1 / sin 30^circ #

# = 2 (\sqrt{3}/2) / (3/sqrt{2}) + 1/(1/2) #

#= 2 + \sqrt{6}/3 = {6+\sqrt{6}}/3 #