What is the value of sec((7pi)/6)-cot((5pi)/6) ?

The value of sec((7pi)/6)-cot((5pi)/6) is -(2sqrt(3))/3+sqrt(3)

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sec((7pi)/6)-cot((5pi)/6)

sec (\frac{7 π}{6}) - cot (\frac{5 π}{6})

- \frac{2 3}{3} + 3

Solution steps

sec (\frac{7 π}{6}) - cot (\frac{5 π}{6})

Rewrite using trig identities:

sec (\frac{7 π}{6}) = - \frac{2 3}{3}

Use the following trivial identity:

cot (\frac{5 π}{6}) = - 3

= - \frac{2 3}{3} - (- 3)

Simplify

= - \frac{2 3}{3} + 3

cot (\frac{6 π}{5})

\frac{13}{tan ( 9 0 ^{\circ} )}

\frac{150}{sin ( 1 5 ^{\circ} )}

tan (21 5^{\circ})

6 sin (\frac{5 π}{4})

What is the value of sec((7pi)/6)-cot((5pi)/6) ?
The value of sec((7pi)/6)-cot((5pi)/6) is -(2sqrt(3))/3+sqrt(3)