Question

What is the exact value of the trigonometric expression in simplest form? cos(-4π/3)/cot (7π/6) - sin(3π/2) tan(3π/4)

Heres a picture

Answer 1

The exact value of the given trigonometric expression in
`simplest form is $(√(3))/(2)+1$.`

The given trigonometric expression is:

`(cos(-(4\pi)/(3)))/(cot((7\pi)/(6)))-sin((3\pi)/(2))tan((3\pi)/(4))`

We can first simplify the individual terms in the expression:

`cos(-(4\pi)/(3)) = -(1)/(2)`

`cot((7\pi)/(6)) = -(√(3))/(3)`

`sin((3\pi)/(2)) = -1`

`tan((3\pi)/(4)) = -1`

Now we can substitute these values into the expression and simplify further:

`(cos(-(4\pi)/(3)))/(cot((7\pi)/(6)))-sin((3\pi)/(2))tan((3\pi)/(4))`

`= (-(1)/(2))/(-(√(3))/(3))-(1)(-1)`

`= (√(3))/(2)+1`