How do you simplify #tan (-5pi / 6) - cot (7pi / 2) #?

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How do you simplify #tan (-5pi / 6) - cot (7pi / 2) #?

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Answer 1 · 2015-11-20T02:45:38

Simplify trig expression.

Ans: #sqrt3/3#

Explanation:

#tan #(-5pi)/6# = tan (pi/6 - (6pi)/6) = tan (pi/6 - pi) = tan (pi/6) = #
# = sqrt3/3.#
#cot ((7pi)/2) = cot ((3pi)/2 + 2pi) = cot ((3pi)/2) = 0#, then
#tan ((-5pi)/6) - cot ((7pi)/2) = sqrt3 - 0 = sqrt3/3#

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How do you simplify #tan (-5pi / 6) - cot (7pi / 2) #?

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